1 Abstract

The HVT package is a collection of R functions to facilitate building topology preserving maps for rich multivariate data analysis. Tending towards a big data preponderance, a large number of rows. A collection of R functions for this typical workflow is organized below:

Data Compression: Vector quantization (VQ), HVQ (hierarchical vector quantization) using means or medians. This step compresses the rows (long data frame) using a compression objective.
Data Projection: Dimension projection of the compressed cells to 1D,2D or Interactive Surface plot with the Sammons Non-linear Algorithm. This step creates topology preserving map (also called as embedding) coordinates into the desired output dimension.
Tessellation: Create cells required for object visualization using the Voronoi Tessellation method, package includes heatmap plots for hierarchical Voronoi tessellations (HVT). This step enables data insights, visualization, and interaction with the topology preserving map. Useful for semi-supervised tasks.
Scoring: Scoring new data sets and recording their assignment using the map objects from the above steps, in a sequence of maps if required.

x	y	z
-2.6282	0.5656	-0.7253
-1.4179	-0.8903	0.9455
-1.0308	1.1066	-0.8731
1.8847	0.1895	0.9944
-1.9506	-2.2507	0.2071
-1.4824	0.9229	0.9672

x	y	z
1.4935	-1.6012	-0.9819
-2.8712	0.3054	0.4609
-1.6231	1.4452	-0.9849
-0.7097	-2.7012	-0.6094
-0.4525	1.1998	0.6964
0.1615	-1.2518	-0.6750

3 Map A : Base Compressed Map

Let us try to visualize the compressed Map A from the flow diagram below.

Figure 1: Data Segregation with highlighted bounding box in red around compressed map A

This package can perform vector quantization using the following algorithms -

Hierarchical Vector Quantization using k−means
Hierarchical Vector Quantization using k−medoids

For more information on vector quantization, refer the following link.

The trainHVT function constructs highly compressed hierarchical Voronoi tessellations. The raw data is first scaled and this scaled data is supplied as input to the vector quantization algorithm. The vector quantization algorithm compresses the dataset until a user-defined compression percentage/rate is achieved using a parameter called quantization error which acts as a threshold and determines the compression percentage. It means that for a given user-defined compression percentage we get the ‘n’ number of cells, then all of these cells formed will have a quantization error less than the threshold quantization error.

Let’s try to comprehend the trainHVT function first before moving ahead.

trainHVT(
  dataset,
  min_compression_perc,
  n_cells,
  depth,
  quant.err,
  distance_metric = c("L1_Norm", "L2_Norm"),
  error_metric = c("mean", "max"),
  quant_method = c("kmeans", "kmedoids"),
  normalize = TRUE,
  diagnose = FALSE,
  hvt_validation = FALSE,
  train_validation_split_ratio = 0.8
)

Each of the parameters of trainHVT function have been explained below:

dataset - A dataframe, with numeric columns (features) that will be used for training the model.
min_compression_perc - An integer, indicating the minimum compression percentage to be achieved for the dataset. It indicates the desired level of reduction in dataset size compared to its original size.
n_cells - An integer, indicating the number of cells per hierarchy (level). This parameter determines the granularity or level of detail in the hierarchical vector quantization.
depth - An integer, indicating the number of levels. A depth of 1 means no hierarchy (single level), while higher values indicate multiple levels (hierarchy).
quant.error - A number indicating the quantization error threshold. A cell will only breakdown into further cells if the quantization error of the cell is above the defined quantization error threshold.
projection.scale - A number indicating the scale factor for the tesselations so as to visualize the sub-tesselations well enough. It helps in adjusting the visual representation of the hierarchy to make the sub-tesselations more visible.
scale_summary - A list with mean and standard deviation values for all the features in the dataset. Pass the scale summary when the input dataset is already scaled or normalize is set to False.
distance_metric - The distance metric can be L1_Norm(Manhattan) or L2_Norm(Eucledian). L1_Norm is selected by default. The distance metric is used to calculate the distance between an n dimensional point and centroid.
error_metric - The error metric can be mean or max. max is selected by default. max will return the max of m values and mean will take mean of m values where each value is a distance between a point and centroid of the cell.
quant_method - The quantization method can be kmeans or kmedoids. Kmeans uses means (centroids) as cluster centers while Kmedoids uses actual data points (medoids) as cluster centers. kmeans is selected by default.
normalize - A logical value indicating if the dataset should be normalized. When set to TRUE, scales the values of all features to have a mean of 0 and a standard deviation of 1 (Z-score)
diagnose - A logical value indicating whether user wants to perform diagnostics on the model. The 4th element of the hvt.result (list) contains detailed informations for debugging. Default value is TRUE.
hvt_validation - A logical value indicating whether user wants to holdout a validation set and find mean absolute deviation of the validation points from the centroid. These values can be found in the 6th element of the hvt.result (list) under the model.info under the title validation_result. Default value is FALSE.
train_validation_split_ratio - A numeric value indicating train validation split ratio. This argument is only used when hvt_validation has been set to TRUE. Default value for the argument is 0.8.

The output of trainHVT function (list of 6 elements) have been explained below:

The ‘1st element’ is a list containing information related to plotting tessellations. This information might include coordinates, boundaries, or other details necessary for visualizing the tessellations
The ‘2nd element’ is a list containing information related to Sammon’s projection coordinates of the data points in the reduced-dimensional space.
The ‘3rd element’ is a list containing detailed information about the hierarchical vector quantized data along with a summary section containing no of points, Quantization Error and the centroids for each cell.
The ‘4th element’ is a list that contains all the diagnostics information of the model when diagnose is set to TRUE.Otherwise NA
The ‘5th element’ is a list that contains all the information required to generates a Mean Absolute Deviation (MAD) plot, if hvt_validation is set to TRUE. Otherwise NA
The ‘6th element’ (model info) is a list that contains model generated timestamp, input parameters passed to the model and the validation results.

We will use the trainHVT function to compress our data while preserving essential features of the dataset. Our goal is to achieve data compression upto atleast 80%. In situations where the compression ratio does not meet the desired target, we can explore adjusting the model parameters as a potential solution. This involves making modifications to parameters such as the quantization error threshold or increasing the number of cells and then rerunning the trainHVT function again.

As this is already done in HVT Vignette: please refer for more information.

Model Parameters

Number of Cells at each Level = 900
Maximum Depth = 1
Quantization Error Threshold = 0.1
Error Metric = Max
Distance Metric = Manhattan

set.seed(240)
torus_mapA <- trainHVT(
  traindata,
  n_cells = 900,
  depth = 1,
  quant.err = 0.1,
  projection.scale = 10,
  normalize = FALSE,
  distance_metric = "L1_Norm",
  error_metric = "max",
  quant_method = "kmeans"
)

Let’s check the compression summary for torus.

compressionSummaryTable(torus_mapA[[3]]$compression_summary)

segmentLevel	noOfCells	noOfCellsBelowQuantizationError	percentOfCellsBelowQuantizationErrorThreshold	parameters
1	900	751	0.83	n_cells: 900 quant.err: 0.1 distance_metric: L1_Norm error_metric: max quant_method: kmeans

We successfully compressed 83% of the data using n_cells parameter as 900, the next step involves performing data projection on the compressed data. In this step, the compressed data will be transformed and projected onto a lower-dimensional space to visualize and analyze the data in a more manageable form.

As per the manual, torus_mapA[[3]] gives us detailed information about the hierarchical vector quantized data. torus_mapA[[3]][['summary']] gives a nice tabular data containing no of points, Quantization Error and the codebook.

The datatable displayed below is the summary from torus_mapA showing Cell.ID, Centroids and Quantization Error for each of the 900 cells.

summaryTable(torus_mapA[[3]]$summary,scroll = TRUE,limit = 500)

Segment.Level	Segment.Parent	Segment.Child	n	Cell.ID	Quant.Error	x	y	z
1	1	1	9	711	0.11	-2.84	0.62	-0.39
1	1	2	17	579	0.1	1.16	0.89	0.84
1	1	3	13	493	0.09	-2.04	0.03	-1.00
1	1	4	9	503	0.07	2.85	0.43	-0.47
1	1	5	7	241	0.05	0.02	-1.27	0.68
1	1	6	13	787	0.11	-2.59	1.15	0.53
1	1	7	14	736	0.11	1.83	1.54	0.91
1	1	8	8	159	0.08	-2.41	-1.35	0.65
1	1	9	13	11	0.12	1.65	-2.45	0.29
1	1	10	7	261	0.05	-0.58	-1.15	-0.70
1	1	11	11	684	0.08	-0.63	1.29	0.83
1	1	12	11	170	0.06	-0.95	-1.68	1.00
1	1	13	14	109	0.12	-2.55	-1.56	0.06
1	1	14	12	443	0.09	-2.22	-0.27	0.97
1	1	15	10	631	0.08	-2.46	0.44	0.86
1	1	16	16	296	0.07	-1.69	-0.85	-0.99
1	1	17	9	826	0.11	2.16	1.98	0.35
1	1	18	16	385	0.08	-1.80	-0.54	-0.99
1	1	19	10	432	0.06	-0.97	-0.25	0.08
1	1	20	10	810	0.08	-1.30	2.00	0.92
1	1	21	6	90	0.06	-0.16	-2.28	-0.96
1	1	22	6	21	0.09	-0.57	-2.92	0.20
1	1	23	9	383	0.1	-2.57	-0.58	0.77
1	1	24	10	160	0.1	-2.62	-1.25	0.41
1	1	25	9	338	0.06	0.95	-0.71	-0.57
1	1	26	11	292	0.06	0.15	-1.01	0.21
1	1	27	12	528	0.07	-1.93	0.23	-0.99
1	1	28	13	781	0.08	0.11	2.03	-1.00
1	1	29	15	197	0.12	-2.83	-0.95	0.10
1	1	30	9	576	0.04	0.49	0.93	-0.30
1	1	31	9	852	0.09	-0.06	2.62	0.78
1	1	32	11	246	0.07	-0.19	-1.24	-0.66
1	1	33	13	440	0.05	-1.12	-0.21	0.51
1	1	34	8	290	0.09	2.31	-0.47	-0.93
1	1	35	13	193	0.09	0.76	-1.40	-0.91
1	1	36	13	599	0.08	-1.94	0.51	-1.00
1	1	37	11	870	0.09	0.91	2.80	-0.30
1	1	38	8	272	0.05	1.16	-0.89	0.84
1	1	39	7	32	0.07	-0.24	-2.81	-0.56
1	1	40	9	280	0.05	0.00	-1.08	0.38
1	1	41	11	333	0.12	2.91	-0.29	0.35
1	1	42	14	877	0.08	1.19	2.74	-0.12
1	1	43	14	526	0.07	0.90	0.64	0.46
1	1	44	16	507	0.08	0.93	0.51	0.36
1	1	45	8	504	0.06	1.26	0.50	-0.76
1	1	46	14	498	0.06	-1.05	0.25	-0.38
1	1	47	16	464	0.09	-1.55	-0.12	0.89
1	1	48	9	682	0.08	-0.06	1.35	0.76
1	1	49	14	373	0.08	-1.22	-0.61	-0.77
1	1	50	10	554	0.09	2.72	0.60	-0.61
1	1	51	9	720	0.08	-0.54	1.52	0.92
1	1	52	10	81	0.09	1.20	-2.16	-0.88
1	1	53	15	780	0.1	1.72	1.83	0.85
1	1	54	9	640	0.06	0.16	1.18	0.58
1	1	55	15	480	0.08	-1.90	-0.02	0.99
1	1	56	6	339	0.06	1.13	-0.66	0.72
1	1	57	6	790	0.05	0.77	2.16	0.95
1	1	58	10	205	0.09	2.91	-0.56	0.27
1	1	59	10	104	0.07	-1.35	-2.11	-0.86
1	1	60	7	153	0.07	-0.58	-1.77	-0.99
1	1	61	6	768	0.05	-0.18	1.92	1.00
1	1	62	9	250	0.06	-0.81	-1.19	-0.83
1	1	63	7	572	0.06	0.46	0.90	-0.13
1	1	64	12	365	0.07	0.86	-0.56	0.25
1	1	65	10	580	0.07	-0.71	0.82	-0.40
1	1	66	13	801	0.13	2.18	1.85	-0.49
1	1	67	8	454	0.09	-2.96	-0.23	0.23
1	1	68	9	243	0.05	-1.47	-1.09	-0.99
1	1	69	13	860	0.12	1.81	2.38	0.03
1	1	70	9	844	0.07	-0.33	2.54	0.83
1	1	71	6	157	0.07	-0.84	-1.74	-1.00
1	1	72	14	435	0.06	1.27	0.00	0.68
1	1	73	18	714	0.12	1.42	1.49	0.99
1	1	74	12	402	0.06	1.17	-0.27	-0.60
1	1	75	8	749	0.09	-2.30	1.07	0.84
1	1	76	9	716	0.1	1.72	1.50	-0.95
1	1	77	10	421	0.1	2.63	0.04	0.77
1	1	78	7	180	0.05	-1.95	-1.40	0.92
1	1	79	12	721	0.09	2.73	1.20	-0.16
1	1	80	16	712	0.08	-2.08	0.94	0.96
1	1	81	6	91	0.08	-0.85	-2.30	-0.89
1	1	82	11	332	0.07	0.55	-0.83	-0.04
1	1	83	13	441	0.06	1.04	0.04	-0.30
1	1	84	6	539	0.06	1.45	0.68	-0.91
1	1	85	11	789	0.08	-2.38	1.30	-0.70
1	1	86	7	626	0.07	-0.11	1.12	-0.49
1	1	87	11	354	0.07	-0.74	-0.77	-0.35
1	1	88	10	368	0.1	-2.89	-0.56	0.31
1	1	89	11	123	0.08	-1.60	-1.85	-0.89
1	1	90	7	77	0.05	-1.17	-2.33	-0.79
1	1	91	12	142	0.07	-1.02	-1.91	0.98
1	1	92	5	195	0.06	-0.33	-1.56	0.91
1	1	93	13	524	0.1	1.06	0.62	0.63
1	1	94	18	637	0.07	1.57	1.04	0.99
1	1	95	8	135	0.06	-1.81	-1.73	0.86
1	1	96	17	895	0.14	-1.36	2.62	0.30
1	1	97	15	848	0.16	-2.46	1.62	0.31
1	1	98	12	627	0.06	0.51	1.12	0.64
1	1	99	6	582	0.09	-2.86	0.20	0.48
1	1	100	12	552	0.11	2.58	0.57	0.76
1	1	101	12	515	0.07	-0.93	0.39	0.16
1	1	102	16	899	0.13	-1.55	2.51	-0.26
1	1	103	8	30	0.09	0.59	-2.72	-0.62
1	1	104	13	143	0.11	-2.70	-1.29	0.05
1	1	105	10	417	0.06	1.08	-0.15	-0.42
1	1	106	11	210	0.06	1.24	-1.18	0.96
1	1	107	5	306	0.04	-0.15	-0.99	0.08
1	1	108	11	565	0.07	-1.39	0.57	-0.86
1	1	109	11	624	0.05	0.24	1.14	-0.55
1	1	110	8	155	0.05	1.91	-1.25	-0.96
1	1	111	12	618	0.07	0.73	1.12	-0.75
1	1	112	11	102	0.09	-1.96	-1.96	0.63
1	1	113	10	670	0.1	-2.69	0.48	0.67
1	1	114	6	238	0.04	1.63	-0.87	0.99
1	1	115	20	422	0.15	-2.09	-0.31	-0.99
1	1	116	8	568	0.08	1.97	0.77	-0.99
1	1	117	10	657	0.04	0.06	1.24	0.65
1	1	118	5	288	0.03	-0.19	-1.06	0.38
1	1	119	12	323	0.07	1.98	-0.50	-1.00
1	1	120	5	632	0.06	-0.22	1.12	0.51
1	1	121	15	172	0.09	2.56	-0.89	-0.70
1	1	122	7	897	0.1	-0.23	2.98	0.07
1	1	123	9	510	0.06	-1.40	0.21	0.81
1	1	124	6	95	0.07	1.72	-1.85	-0.85
1	1	125	9	424	0.07	1.70	-0.02	-0.95
1	1	126	15	372	0.05	1.20	-0.42	0.68
1	1	127	10	818	0.11	-2.67	1.30	0.25
1	1	128	13	94	0.11	-2.32	-1.81	0.30
1	1	129	12	797	0.09	0.72	2.22	-0.94
1	1	130	9	745	0.08	2.18	1.53	-0.74
1	1	131	11	60	0.08	-0.25	-2.59	-0.80
1	1	132	13	532	0.09	-1.09	0.49	-0.59
1	1	133	11	264	0.08	0.61	-1.05	0.62
1	1	134	13	643	0.09	0.37	1.25	-0.72
1	1	135	17	884	0.13	-2.18	2.02	0.17
1	1	136	12	531	0.07	-1.33	0.38	0.79
1	1	137	6	287	0.05	-0.71	-1.03	-0.67
1	1	138	11	541	0.07	0.92	0.73	-0.56
1	1	139	15	837	0.12	1.82	2.20	0.51
1	1	140	13	55	0.1	2.27	-1.86	0.34
1	1	141	18	630	0.07	1.33	1.07	0.95
1	1	142	10	704	0.06	-0.35	1.44	0.85
1	1	143	8	304	0.06	-0.35	-1.00	-0.34
1	1	144	12	587	0.09	0.62	0.95	0.50
1	1	145	12	298	0.05	-0.59	-1.01	-0.55
1	1	146	9	659	0.12	-2.82	0.38	-0.52
1	1	147	11	828	0.11	-2.66	1.38	0.03
1	1	148	9	218	0.06	-0.80	-1.35	-0.90
1	1	149	9	233	0.08	0.98	-1.13	-0.86
1	1	150	16	567	0.08	-0.68	0.75	0.17
1	1	151	9	364	0.08	2.61	-0.23	0.78
1	1	152	9	49	0.06	-1.17	-2.58	-0.55
1	1	153	7	458	0.08	2.40	0.18	0.91
1	1	154	14	851	0.09	-0.02	2.62	-0.78
1	1	155	9	377	0.06	0.88	-0.50	-0.15
1	1	156	8	680	0.05	-0.49	1.33	-0.81
1	1	157	12	616	0.08	-0.58	0.98	0.51
1	1	158	12	778	0.1	-2.81	1.01	-0.10
1	1	159	8	17	0.07	0.21	-2.90	0.42
1	1	160	14	51	0.12	-2.03	-2.19	-0.10
1	1	161	12	192	0.07	1.15	-1.29	-0.96
1	1	162	17	628	0.1	-0.93	0.95	0.73
1	1	163	10	392	0.05	1.02	-0.35	0.39
1	1	164	9	136	0.07	0.25	-1.85	-0.99
1	1	165	12	258	0.09	0.33	-1.16	0.60
1	1	166	14	707	0.07	1.01	1.59	-0.99
1	1	167	14	890	0.12	0.01	2.94	-0.30
1	1	168	3	654	0.05	2.55	0.94	-0.69
1	1	169	11	134	0.09	-1.93	-1.63	-0.85
1	1	170	13	53	0.11	1.91	-2.07	0.56
1	1	171	7	892	0.08	-0.58	2.89	0.31
1	1	172	10	115	0.09	1.74	-1.67	0.91
1	1	173	5	689	0.05	-0.69	1.37	-0.88
1	1	174	10	369	0.07	-0.76	-0.66	-0.14
1	1	175	15	394	0.08	1.33	-0.27	0.77
1	1	176	10	455	0.07	1.93	0.16	-0.99
1	1	177	10	506	0.06	0.87	0.52	0.13
1	1	178	11	488	0.05	1.08	0.35	0.51
1	1	179	13	431	0.07	1.49	0.00	0.86
1	1	180	13	658	0.08	-0.34	1.19	0.65
1	1	181	13	469	0.09	2.77	0.25	0.61
1	1	182	8	804	0.09	1.11	2.20	0.88
1	1	183	6	319	0.05	1.01	-0.80	0.70
1	1	184	17	473	0.06	-1.01	0.10	0.19
1	1	185	10	177	0.08	1.42	-1.34	1.00
1	1	186	15	569	0.07	0.53	0.88	0.22
1	1	187	12	148	0.08	0.14	-1.82	0.98
1	1	188	7	811	0.12	1.80	2.07	-0.66
1	1	189	12	698	0.08	2.02	1.31	-0.91
1	1	190	9	444	0.05	-1.20	-0.15	-0.61
1	1	191	10	154	0.06	-1.41	-1.65	-0.98
1	1	192	6	513	0.08	0.95	0.54	-0.44
1	1	193	11	382	0.1	2.37	-0.19	0.92
1	1	194	8	845	0.09	-2.51	1.56	-0.27
1	1	195	14	295	0.07	-1.16	-1.01	0.89
1	1	196	12	649	0.09	-1.36	0.86	0.92
1	1	197	11	891	0.12	-0.63	2.87	-0.32
1	1	198	8	702	0.07	2.00	1.26	0.93
1	1	199	12	307	0.04	0.49	-0.92	-0.30
1	1	200	16	318	0.05	0.76	-0.84	-0.50
1	1	201	12	366	0.12	-2.30	-0.63	0.92
1	1	202	13	300	0.1	2.22	-0.49	0.96
1	1	203	9	461	0.08	2.35	0.18	-0.93
1	1	204	8	259	0.04	0.40	-1.12	-0.58
1	1	205	13	731	0.07	1.05	1.68	1.00
1	1	206	11	325	0.06	0.52	-0.87	0.15
1	1	207	16	857	0.13	-2.04	1.94	0.57
1	1	208	14	358	0.06	-0.68	-0.77	0.23
1	1	209	8	331	0.06	-0.65	-0.93	0.51
1	1	210	13	462	0.06	0.99	0.16	0.01
1	1	211	6	252	0.06	2.50	-0.54	0.83
1	1	212	13	706	0.08	-1.44	1.24	-0.99
1	1	213	7	430	0.05	1.01	-0.07	0.15
1	1	214	8	521	0.05	0.81	0.60	0.06
1	1	215	14	44	0.1	-0.25	-2.78	0.61
1	1	216	11	596	0.06	-0.41	0.94	-0.24
1	1	217	12	82	0.08	0.78	-2.33	0.89
1	1	218	7	796	0.06	-0.82	2.06	-0.97
1	1	219	6	829	0.08	0.05	2.44	0.90
1	1	220	14	381	0.08	1.60	-0.29	0.92
1	1	221	18	35	0.12	-0.99	-2.81	0.17
1	1	222	12	570	0.07	-0.66	0.77	-0.13
1	1	223	10	209	0.1	-2.81	-0.88	-0.30
1	1	224	13	832	0.1	-0.33	2.43	-0.89
1	1	225	17	896	0.15	-1.94	2.24	0.20
1	1	226	16	14	0.1	-0.28	-2.98	-0.05
1	1	227	16	389	0.08	-1.06	-0.54	-0.59
1	1	228	13	619	0.06	0.34	1.08	0.51
1	1	229	12	751	0.09	1.73	1.71	-0.90
1	1	230	8	757	0.05	-0.65	1.81	-0.99
1	1	231	21	677	0.09	-2.26	0.65	0.93
1	1	232	8	438	0.07	-2.70	-0.31	0.69
1	1	233	9	89	0.07	0.12	-2.28	-0.95
1	1	234	9	847	0.11	1.25	2.53	-0.56
1	1	235	6	598	0.06	-0.58	0.92	-0.41
1	1	236	11	67	0.1	1.93	-1.96	-0.65
1	1	237	12	448	0.05	1.07	0.09	0.37
1	1	238	9	149	0.08	2.32	-1.15	0.80
1	1	239	6	346	0.05	-0.70	-0.83	0.40
1	1	240	6	322	0.04	1.29	-0.69	0.84
1	1	241	9	820	0.1	-0.92	2.20	0.92
1	1	242	9	116	0.09	2.49	-1.32	0.56
1	1	243	15	133	0.08	1.16	-1.79	0.99
1	1	244	11	450	0.07	1.53	0.12	-0.89
1	1	245	9	303	0.05	0.38	-0.96	0.25
1	1	246	12	841	0.12	2.13	2.10	0.09
1	1	247	8	562	0.04	0.66	0.85	-0.38
1	1	248	12	543	0.09	1.37	0.68	0.88
1	1	249	10	412	0.09	2.90	0.00	0.42
1	1	250	11	64	0.11	-0.71	-2.63	0.68
1	1	251	8	646	0.05	0.81	1.26	-0.86
1	1	252	10	585	0.05	0.34	0.97	-0.23
1	1	253	12	694	0.08	1.18	1.42	0.99
1	1	254	7	674	0.09	2.73	0.95	-0.44
1	1	255	8	889	0.08	0.14	2.96	0.25
1	1	256	12	760	0.08	2.15	1.56	0.75
1	1	257	10	37	0.09	1.29	-2.48	-0.60
1	1	258	7	26	0.09	-0.58	-2.85	-0.41
1	1	259	21	559	0.12	1.75	0.70	0.99
1	1	260	11	625	0.08	1.85	0.98	-0.99
1	1	261	9	629	0.06	-1.54	0.78	-0.96
1	1	262	12	386	0.07	1.85	-0.25	-0.99
1	1	263	7	647	0.07	-1.77	0.69	0.99
1	1	264	15	609	0.06	0.07	1.03	0.26
1	1	265	10	537	0.08	-2.25	0.20	-0.96
1	1	266	13	766	0.06	-1.58	1.54	0.98
1	1	267	14	146	0.08	1.70	-1.43	-0.97
1	1	268	10	621	0.05	0.06	1.08	0.40
1	1	269	15	52	0.11	0.97	-2.54	0.69
1	1	270	7	12	0.06	0.65	-2.86	-0.35
1	1	271	12	509	0.06	-1.00	0.33	0.31
1	1	272	13	880	0.1	-1.05	2.64	-0.52
1	1	273	4	563	0.03	0.58	0.85	-0.25
1	1	274	7	785	0.06	-0.49	2.01	-1.00
1	1	275	12	802	0.1	2.05	1.87	0.62
1	1	276	11	270	0.06	0.88	-0.99	0.74
1	1	277	12	550	0.06	-0.79	0.62	-0.08
1	1	278	7	10	0.08	0.01	-2.99	0.07
1	1	279	10	101	0.09	2.66	-1.38	0.02
1	1	280	10	871	0.08	1.16	2.71	0.30
1	1	281	10	754	0.11	0.70	1.88	-0.99
1	1	282	9	825	0.08	-1.81	1.86	0.80
1	1	283	15	561	0.07	0.84	0.81	0.55
1	1	284	10	237	0.07	-0.47	-1.32	0.80
1	1	285	16	660	0.08	1.05	1.22	0.92
1	1	286	10	540	0.05	0.71	0.72	-0.13
1	1	287	10	776	0.11	2.52	1.55	0.24
1	1	288	11	717	0.05	-0.60	1.56	-0.94
1	1	289	8	167	0.08	-1.20	-1.67	0.99
1	1	290	8	471	0.06	1.04	0.29	0.38
1	1	291	7	36	0.07	-1.37	-2.60	-0.33
1	1	292	14	642	0.07	-0.30	1.18	-0.62
1	1	293	11	2	0.12	1.84	-2.36	0.02
1	1	294	12	449	0.07	-1.52	-0.14	-0.88
1	1	295	11	106	0.09	1.98	-1.63	-0.82
1	1	296	11	875	0.11	-0.77	2.69	0.59
1	1	297	12	48	0.11	-1.80	-2.32	-0.33
1	1	298	16	42	0.1	-1.34	-2.61	0.34
1	1	299	20	16	0.13	1.23	-2.63	0.41
1	1	300	8	575	0.07	-1.75	0.42	0.98
1	1	301	10	713	0.1	2.58	1.24	-0.51
1	1	302	12	900	0.12	-1.19	2.74	0.00
1	1	303	9	248	0.05	0.01	-1.20	-0.60
1	1	304	10	284	0.05	0.01	-1.05	-0.30
1	1	305	8	345	0.08	1.83	-0.42	0.99
1	1	306	8	45	0.09	2.11	-2.00	-0.41
1	1	307	9	232	0.07	0.21	-1.30	0.73
1	1	308	9	740	0.06	-1.65	1.30	0.99
1	1	309	6	279	0.05	-0.41	-1.07	-0.52
1	1	310	12	163	0.09	-0.32	-1.73	-0.97
1	1	311	17	108	0.11	-0.52	-2.15	-0.97
1	1	312	13	434	0.05	-1.03	-0.26	0.35
1	1	313	26	257	0.1	1.55	-0.81	-0.96
1	1	314	14	78	0.1	-0.46	-2.48	0.85
1	1	315	8	607	0.04	0.34	1.07	-0.47
1	1	316	13	833	0.1	2.04	2.12	-0.32
1	1	317	8	514	0.06	-2.18	0.07	0.98
1	1	318	19	876	0.13	-2.19	1.93	-0.36
1	1	319	14	401	0.1	2.26	-0.13	-0.96
1	1	320	16	874	0.12	-0.30	2.77	-0.61
1	1	321	11	398	0.07	1.30	-0.26	-0.74
1	1	322	9	390	0.06	1.05	-0.36	-0.46
1	1	323	10	367	0.06	1.00	-0.50	0.47
1	1	324	9	809	0.08	-1.58	1.85	0.90
1	1	325	10	396	0.09	-1.44	-0.52	0.88
1	1	326	8	253	0.06	0.56	-1.13	-0.67
1	1	327	5	792	0.03	-0.45	2.07	0.99
1	1	328	14	156	0.07	0.39	-1.73	0.97
1	1	329	13	231	0.08	2.04	-0.75	-0.98
1	1	330	5	499	0.03	1.96	0.40	-1.00
1	1	331	14	842	0.08	-0.88	2.42	0.82
1	1	332	7	260	0.06	-0.17	-1.19	0.60
1	1	333	9	683	0.12	-2.89	0.46	0.36
1	1	334	15	314	0.06	0.38	-0.93	0.05
1	1	335	8	574	0.05	0.79	0.92	-0.61
1	1	336	11	533	0.05	-0.85	0.53	0.06
1	1	337	16	752	0.09	1.04	1.86	-0.99
1	1	338	9	691	0.07	-2.00	0.89	-0.98
1	1	339	7	813	0.06	0.16	2.28	0.96
1	1	340	12	459	0.05	1.01	0.15	0.19
1	1	341	12	151	0.07	1.17	-1.55	-1.00
1	1	342	19	436	0.07	-1.36	-0.28	0.79
1	1	343	16	551	0.07	-0.87	0.61	-0.35
1	1	344	9	378	0.06	0.89	-0.48	0.16
1	1	345	10	265	0.05	0.13	-1.10	-0.46
1	1	346	18	494	0.09	1.23	0.40	0.71
1	1	347	9	710	0.05	0.55	1.55	0.94
1	1	348	3	8	0.07	0.36	-2.93	-0.28
1	1	349	7	9	0.07	0.14	-2.96	-0.27
1	1	350	9	315	0.03	-0.37	-0.98	0.31
1	1	351	12	226	0.07	0.67	-1.24	-0.81
1	1	352	10	648	0.08	-1.76	0.75	-0.99
1	1	353	11	293	0.06	-0.10	-1.04	0.28
1	1	354	22	693	0.08	0.75	1.53	-0.95
1	1	355	8	150	0.08	-0.07	-1.76	-0.97
1	1	356	9	212	0.04	1.65	-1.00	1.00
1	1	357	11	556	0.07	-2.62	0.16	0.78
1	1	358	8	5	0.07	0.37	-2.97	0.10
1	1	359	11	463	0.06	-1.17	-0.06	0.55
1	1	360	13	351	0.06	-0.61	-0.79	-0.02
1	1	361	8	173	0.06	1.22	-1.44	0.99
1	1	362	13	33	0.09	-0.86	-2.80	-0.35
1	1	363	8	356	0.06	0.79	-0.66	-0.24
1	1	364	14	69	0.11	-1.64	-2.31	0.55
1	1	365	7	779	0.08	2.32	1.63	0.54
1	1	366	15	128	0.11	-2.18	-1.67	0.66
1	1	367	11	25	0.09	0.01	-2.84	-0.53
1	1	368	8	220	0.05	-0.58	-1.36	-0.85
1	1	369	7	249	0.08	1.22	-0.97	-0.90
1	1	370	13	816	0.12	-1.25	2.08	-0.90
1	1	371	4	254	0.07	-0.43	-1.20	-0.69
1	1	372	6	273	0.06	1.42	-0.77	0.92
1	1	373	9	661	0.06	-0.66	1.18	-0.76
1	1	374	10	611	0.04	-1.30	0.76	-0.87
1	1	375	7	795	0.06	-0.36	2.13	-0.99
1	1	376	12	692	0.07	2.82	1.02	0.08
1	1	377	14	86	0.11	1.41	-2.01	-0.88
1	1	378	12	251	0.07	-1.38	-1.14	0.98
1	1	379	8	517	0.05	-1.01	0.39	-0.39
1	1	380	13	119	0.1	0.92	-1.89	-0.99
1	1	381	13	240	0.06	0.25	-1.23	-0.67
1	1	382	12	140	0.07	0.62	-1.84	1.00
1	1	383	10	363	0.07	1.09	-0.53	-0.62
1	1	384	13	357	0.08	0.75	-0.67	-0.03
1	1	385	13	46	0.11	1.52	-2.33	0.62
1	1	386	5	723	0.11	-2.53	0.82	-0.74
1	1	387	10	725	0.07	2.61	1.21	0.47
1	1	388	12	885	0.11	0.31	2.94	-0.28
1	1	389	11	465	0.09	2.63	0.21	-0.76
1	1	390	16	439	0.08	-2.49	-0.30	0.86
1	1	391	10	374	0.06	-0.77	-0.64	0.05
1	1	392	8	62	0.08	-1.17	-2.57	0.55
1	1	393	13	853	0.09	1.02	2.62	0.58
1	1	394	15	278	0.07	-0.13	-1.07	-0.38
1	1	395	9	746	0.06	-0.30	1.71	0.96
1	1	396	13	544	0.07	-0.86	0.58	0.26
1	1	397	10	176	0.11	2.72	-0.80	0.53
1	1	398	8	235	0.07	-0.17	-1.32	0.74
1	1	399	10	671	0.1	-2.60	0.52	-0.76
1	1	400	13	588	0.08	-1.03	0.75	0.68
1	1	401	10	117	0.08	0.26	-2.09	0.99
1	1	402	15	187	0.09	1.74	-1.09	-1.00
1	1	403	12	846	0.11	1.54	2.41	-0.50
1	1	404	8	817	0.08	0.58	2.34	0.91
1	1	405	6	788	0.07	-1.38	1.82	-0.96
1	1	406	5	605	0.03	0.21	1.06	-0.39
1	1	407	11	516	0.07	-0.93	0.40	-0.19
1	1	408	9	523	0.05	0.83	0.62	-0.25
1	1	409	6	202	0.05	-1.01	-1.43	-0.97
1	1	410	5	416	0.04	0.98	-0.19	0.00
1	1	411	12	408	0.07	-1.23	-0.46	0.73
1	1	412	7	475	0.07	-1.35	0.04	0.76
1	1	413	5	814	0.06	0.35	2.30	0.94
1	1	414	7	207	0.06	-0.63	-1.46	0.91
1	1	415	10	733	0.08	-2.19	1.08	-0.89
1	1	416	11	867	0.07	0.28	2.77	0.62
1	1	417	12	468	0.12	1.58	0.23	0.91
1	1	418	11	474	0.08	1.37	0.31	-0.80
1	1	419	8	113	0.12	2.53	-1.29	-0.54
1	1	420	7	615	0.05	0.11	1.10	-0.44
1	1	421	10	722	0.06	0.04	1.60	0.92
1	1	422	13	482	0.07	-1.00	0.15	-0.16
1	1	423	9	97	0.09	1.03	-2.09	-0.94
1	1	424	16	222	0.07	0.36	-1.30	-0.76
1	1	425	9	201	0.07	2.41	-0.78	0.84
1	1	426	10	858	0.13	-1.67	2.17	0.66
1	1	427	10	426	0.05	-0.97	-0.28	-0.15
1	1	428	8	329	0.05	-0.39	-0.92	0.00
1	1	429	10	125	0.08	0.00	-1.98	-1.00
1	1	430	13	376	0.08	-1.91	-0.62	1.00
1	1	431	17	388	0.08	-1.70	-0.56	0.98
1	1	432	6	92	0.06	0.05	-2.34	0.94
1	1	433	10	141	0.07	-0.36	-1.93	1.00
1	1	434	11	490	0.1	1.44	0.37	0.86
1	1	435	7	774	0.05	-0.43	1.92	1.00
1	1	436	13	491	0.09	-1.64	0.08	-0.93
1	1	437	4	782	0.04	-1.86	1.48	0.92
1	1	438	8	330	0.04	-0.51	-0.92	0.32
1	1	439	14	850	0.08	0.46	2.63	0.74
1	1	440	15	610	0.06	0.95	1.06	-0.81
1	1	441	7	639	0.08	2.57	0.86	0.70
1	1	442	2	289	0.02	-0.39	-1.06	0.50
1	1	443	12	739	0.06	-1.94	1.18	0.96
1	1	444	17	602	0.09	1.17	1.02	-0.89
1	1	445	12	400	0.09	-2.95	-0.45	-0.16
1	1	446	8	127	0.1	-0.84	-2.08	0.97
1	1	447	5	676	0.05	-0.84	1.23	-0.86
1	1	448	7	41	0.1	-1.73	-2.42	0.18
1	1	449	15	425	0.09	-1.73	-0.29	-0.97
1	1	450	15	888	0.11	-1.58	2.43	0.44
1	1	451	9	217	0.07	2.36	-0.71	-0.88
1	1	452	8	771	0.08	1.30	1.91	0.95
1	1	453	9	859	0.1	-1.22	2.43	0.69
1	1	454	15	311	0.1	-1.98	-0.80	-0.99
1	1	455	15	230	0.08	-2.43	-0.89	-0.80
1	1	456	11	703	0.08	0.28	1.50	0.88
1	1	457	8	672	0.06	2.82	0.93	-0.23
1	1	458	5	182	0.06	-1.74	-1.41	0.97
1	1	459	12	100	0.1	-0.89	-2.34	0.86
1	1	460	16	124	0.11	2.73	-1.15	-0.24
1	1	461	14	697	0.07	-1.72	1.06	-1.00
1	1	462	7	262	0.04	0.05	-1.15	0.53
1	1	463	11	247	0.06	-0.75	-1.25	0.84
1	1	464	15	457	0.07	1.15	0.15	0.54
1	1	465	8	348	0.07	1.52	-0.50	-0.92
1	1	466	6	19	0.07	-0.64	-2.93	-0.06
1	1	467	12	535	0.08	2.52	0.57	-0.81
1	1	468	13	470	0.08	2.04	0.28	0.99
1	1	469	6	665	0.06	2.11	1.09	-0.92
1	1	470	14	83	0.1	-1.33	-2.34	0.72
1	1	471	5	344	0.04	0.98	-0.67	0.58
1	1	472	6	519	0.05	1.59	0.53	-0.94
1	1	473	12	228	0.08	0.99	-1.19	0.89
1	1	474	6	663	0.04	0.34	1.27	0.72
1	1	475	17	601	0.06	-0.04	1.00	-0.02
1	1	476	10	203	0.06	-1.46	-1.31	-1.00
1	1	477	8	865	0.11	-0.35	2.70	0.69
1	1	478	10	653	0.06	-0.90	1.11	-0.82
1	1	479	7	204	0.08	2.88	-0.59	-0.33
1	1	480	15	340	0.11	-2.69	-0.65	-0.63
1	1	481	15	744	0.08	-1.22	1.56	-1.00
1	1	482	13	822	0.11	-1.88	1.79	-0.80
1	1	483	9	589	0.07	0.56	0.99	-0.51
1	1	484	12	549	0.07	0.70	0.75	0.24
1	1	485	7	110	0.09	0.53	-2.08	0.98
1	1	486	8	291	0.04	0.14	-1.01	-0.20
1	1	487	21	586	0.08	0.26	0.97	0.08
1	1	488	13	666	0.09	1.40	1.26	-0.99
1	1	489	11	349	0.08	-0.92	-0.78	-0.61
1	1	490	9	171	0.08	-1.75	-1.42	-0.97
1	1	491	8	635	0.05	-0.52	1.12	-0.64
1	1	492	11	487	0.06	0.95	0.36	0.17
1	1	493	14	767	0.13	2.54	1.53	-0.23
1	1	494	17	175	0.07	0.64	-1.57	0.95
1	1	495	14	96	0.12	-2.30	-1.76	-0.42
1	1	496	9	428	0.04	-1.03	-0.25	-0.34
1	1	497	10	447	0.05	1.00	0.08	-0.12
1	1	498	10	466	0.1	2.97	0.21	-0.20
1	1	499	10	879	0.13	-1.37	2.46	-0.56
1	1	500	12	806	0.11	-2.61	1.27	-0.42

Now let us understand what each column in the above table means:

Segment.Level - Level of the cell. In this case, we have performed Vector Quantization for depth 1. Hence Segment Level is 1.
Segment.Parent - Parent segment of the cell.
Segment.Child (Cell.Number) - The children of a particular cell. In this case, it is the total number of cells at which we achieved the defined compression percentage.
n - No of points in each cell.
Cell.ID - Cell_ID’s are generated for the multivariate data using 1-D Sammon’s Projection algorithm.
Quant.Error - Quantization Error for each cell.

All the columns after this will contain centroids for each cell. They can also be called a codebook, which represents a collection of all centroids or codewords.

Now, let’s check the compression summary for HVT (torus_mapA) where n_cell was set to 900. The table below shows no of cells, no of cells having quantization error below threshold and percentage of cells having quantization error below threshold for each level.

mapA_compression_summary <- torus_mapA[[3]]$compression_summary %>%  dplyr::mutate_if(is.numeric, funs(round(.,4)))
compressionSummaryTable(mapA_compression_summary)

segmentLevel	noOfCells	noOfCellsBelowQuantizationError	percentOfCellsBelowQuantizationErrorThreshold	parameters
1	900	751	0.83	n_cells: 900 quant.err: 0.1 distance_metric: L1_Norm error_metric: max quant_method: kmeans

As it can be seen from the table above, 83% of the cells have hit the quantization threshold error.Since we are successfully able to attain the desired compression percentage, so we will not further subdivide the cells

Now let’s try to understand plotHVT function. The parameters have been explained in detail below:

plotHVT <-(hvt.results, line.width, color.vec, pch1 = 21, palette.color = 6, centroid.size = 1.5, title = NULL, maxDepth = NULL, dataset, child.level, hmap.cols, previous_level_heatmap = TRUE, show.points = FALSE, asp = 1, ask = TRUE, tess.label = NULL, quant.error.hmap = NULL, n_cells.hmap = NULL, label.size = 0.5, sepration_width = 7, layer_opacity = c(0.5, 0.75, 0.99), dim_size = 1000, heatmap = '2DHVT')

hvt.results - (1D/2D/Surface_plot) A list (hvt.result) obtained from the trainHVT function while performing hierarchical vector quantization on training data. This list provides an overview of the hierarchical vector quantized data, including diagnostics, tessellation details, Sammon’s projection coordinates, and model input information.
line.width - (2D) A vector indicating the line widths of the tessellation boundaries for each layer.
color.vec - (2D) A vector indicating the colors of the tessellations boundaries at each layer.
pch1 - (2D) Symbol, It plots the centroids with a particular symbol such as (solid circle, bullet, filled square, filled diamond) in the tessellations.(default = 21 i.e filled circle).
centroid.size - (2D) Size of centroids for each level of tessellations (default = 3).
title - (2DHVT) Set a title for the plot (default = NULL).
maxDepth - (2DHVT) An integer indicating the number of levels. (default = NULL)
palette.color - (2DHEATMAP) A number indicating the heat map color palette. 1 - rainbow,2 - heat.colors, 3 - terrain.colors, 4 - topo.colors, 5 - cm.colors, 6 - BlCyGrYlRd (Blue,Cyan,Green,Yellow,Red) color (default= 6).
dataset - (2DHEATMAP) Data frame. The input dataset.
child.level - (2DHEATMAP/Surface_plot) A Number indicating the level for which the heat map is to be plotted.
hmap.cols - (2DHEATMAP/Surface_plot) A Number or a Character which is the column number of column name from the dataset indicating the variables for which the heat map is to be plotted.
previous_level_heatmap - (2DHEATMAP) A Logical value to indicate whether the heatmap of previous level will be overlayed on the heatmap of selected level.
show.points - (2DHEATMAP) A Logical value indicating if the centroids should be plotted on the tessellations. (default = FALSE)
asp - (2DHEATMAP) A Number indicating the aspect ratio type. For flexible aspect ratio set, asp = NA. (default = 1)
ask - (2DHEATMAP) A Logical value to have interactive R session.(default = TRUE)
tess.label - (2DHEATMAP) A vector for labelling the tessellations. (default = NULL)
label.size - (2DHEATMAP) The size by which the tessellation labels should be scaled.(default = 0.5)
quant.error.hmap - (2DHEATMAP) A number indicating the quantization error threshold.
n_cells.hmap - (2DHEATMAP) An integer indicating the number of cells/clusters per hierarchy
sepration_width - (Surface_plot) An integer indicating the width between two Levels.
layer_opacity - (Surface_plot) A vector indicating the opacity of each layer/ level.
dim_size - (Surface_plot) An integer indicating the dimension size used to create the matrix for the plot.
heatmap - A Character indicating which type of plot should be generated. Accepted entries are ‘1D’,‘2DHVT’,‘2DHEATMAP’, ‘Surface_plot’. Default value is 2DHVT.

Let’s plot the Voronoi tessellation for layer 1 (map A).

plotHVT(torus_mapA,
        line.width = c(0.4), 
        color.vec = c("#141B41"),
        centroid.size = 0.01,
        maxDepth = 1, heatmap = '2DHVT')

Figure 2: The Voronoi Tessellation for layer 1 (map A) shown for the 900 cells in the dataset ’computers’

Heat Maps

We will now overlay all the features as heatmap over the Voronoi Tessellation plot for better visualization and identification of patterns, trends, and variations in the data.

Now let’s plot the Voronoi Tessellation with the heatmap overlaid for all the features in the torus data for better visualization and interpretation of data patterns and distributions.

The heatmaps displayed below provides a visual representation of the spatial characteristics of the computers data, allowing us to observe patterns and trends in the distribution of each of the features (n,price,speed,hd,ram,screen,ads). The sheer green shades highlight regions with higher values in each of the heatmaps, while the indigo shades indicate areas with the lowest values in each of the heatmaps. By analyzing these heatmaps, we can gain insights into the variations and relationships between each of these features within the computers data.


  plotHVT(
  torus_mapA,
  traindata,
  child.level = 1,
  hmap.cols = "x",
  line.width = c(0.2),
  color.vec = c("#141B41"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = TRUE,
  quant.error.hmap = 0.2,
  n_cells.hmap = 900,
  heatmap = '2DHEATMAP'
)

Figure 4: The Voronoi Tessellation with the heat map overlaid for variable ’x’ in the ’torus’ dataset


  plotHVT(
  torus_mapA,
  traindata,
  child.level = 1,
  hmap.cols = "y",
  line.width = c(0.2),
  color.vec = c("#141B41"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = TRUE,
  quant.error.hmap = 0.2,
  n_cells.hmap = 900,
  heatmap = '2DHEATMAP'
)

Figure 5: The Voronoi Tessellation with the heat map overlaid for variable ’y’ in the ’torus’ dataset


  plotHVT(
  torus_mapA,
  traindata,
  child.level = 1,
  hmap.cols = "z",
  line.width = c(0.2),
  color.vec = c("#141B41"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = TRUE,
  quant.error.hmap = 0.2,
  n_cells.hmap = 440,
  heatmap = '2DHEATMAP'
)

Figure 6: The Voronoi Tessellation with the heat map overlaid for variable ’z’ in the ’torus’ dataset

4 Map B : Compressed Novelty Map

Let us try to visualize the Map B from the flow diagram below.

Figure 10: Data Segregation with highlighted bounding box in red around map B

In this section, we will manually figure out the novelty cells from the plotted torus_mapA and store it in identified_Novelty_cells variable.

Note: For manual selecting the novelty cells from map A, one can enhance its interactivity by adding plotly elements to the code. This will transform map A into an interactive plot, allowing users to actively engage with the data. By hovering over the centroids of the cells, a tag containing segment child information will be displayed. Users can explore the map by hovering over different cells and selectively choose the novelty cells they wish to consider. Added an image for reference.

Figure 11: Manually selecting novelty cells

The removeNovelty function removes the identified novelty cell(s) from the training dataset (containing 9600 datapoints) and stores those records separately.

It takes input as the cell number (Segment.Child) of the manually identified novelty cell(s) and the compressed HVT map (torus_mapA) with 900 cells. It returns a list of two items: data with novelty, and a subset of the data without novelty.

NOTE: As we are using torus data here, the identified novelty cells here given are for demo purpose.

identified_Novelty_cells <<- c(69,246,279,293,573,883,706,745)   #as a example
output_list <- removeNovelty(identified_Novelty_cells, torus_mapA)
data_with_novelty <- output_list[[1]]
data_without_novelty <- output_list[[2]]

Let’s have a look at the data with novelty(containing 99 records). For the sake of brevity, we will only show the first 20 rows.

novelty_data <- data_with_novelty
novelty_data$Row.No <- row.names(novelty_data)
novelty_data <- novelty_data %>% dplyr::select("Row.No","Cell.ID","Cell.Number","x","y","z")
colnames(novelty_data) <- c("Row.No","Cell.ID","Segment.Child","x","y","z")
novelty_data %>% head(100) %>% 
  as.data.frame() %>%
  Table(scroll = TRUE, limit = 20)

Row.No	Cell.ID	Segment.Child	x	y	z
1	860	69	1.8040	2.3903	-0.1035
2	860	69	1.8377	2.3630	0.1140
3	860	69	1.8568	2.3561	-0.0185
4	860	69	1.7230	2.4524	0.0754
5	860	69	1.8535	2.3453	-0.1458
6	860	69	1.7133	2.4573	0.0938
7	860	69	1.7514	2.4179	0.1694
8	860	69	1.6960	2.4726	0.0574
9	860	69	1.8780	2.3255	0.1472
10	860	69	1.8998	2.3110	0.1290
11	860	69	1.9351	2.2918	-0.0300
12	860	69	1.6999	2.4717	-0.0212
13	860	69	1.9299	2.2848	-0.1352
14	841	246	2.1032	2.1328	0.0955
15	841	246	2.1324	2.1102	-0.0032
16	841	246	2.1935	2.0402	0.0928
17	841	246	1.9725	2.2469	0.1419
18	841	246	2.2502	1.9782	0.0877
19	841	246	2.1590	2.0823	0.0300
20	841	246	2.0956	2.1403	0.0963

4.1 Voronoi Tessellation with highlighted novelty cell

The plotNovelCells function is used to plot the Voronoi tessellation using the compressed HVT map (torus_mapA) containing 900 cells and highlights the identified novelty cell(s) i.e 8 cells (containing 99 records) in red on the map.

plotNovelCells(identified_Novelty_cells, torus_mapA,line.width = c(0.4),centroid.size = 0.01)

Figure 12: The Voronoi Tessellation constructed using the compressed HVT map (map A) with the novelty cell(s) highlighted in red

We pass the dataframe with novelty records (99 records) to trainHVT function along with other model parameters mentioned below to generate map B (layer2)

Model Parameters

Number of Cells at each Level = 6
Maximum Depth = 1
Quantization Error Threshold = 0.2
Error Metric = Max
Distance Metric = Manhattan

colnames(data_with_novelty) <- c("Cell.ID","Segment.Child","x","y","z")
data_with_novelty <- data_with_novelty[,-1:-2]
torus_mapB <- list()
mapA_scale_summary = torus_mapA[[3]]$scale_summary
torus_mapB <- trainHVT(data_with_novelty,
                  n_cells = 6,   
                  depth = 1,
                  quant.err = 0.2,
                  projection.scale = 10,
                  normalize = FALSE,
                  distance_metric = "L1_Norm",
                  error_metric = "max",
                  quant_method = "kmeans",
                  diagnose = FALSE
                  )

The datatable displayed below is the summary from map B (layer 2) showing Cell.ID, Centroids and Quantization Error for each of the 6 cells.

summaryTable(torus_mapB[[3]]$summary,scroll = TRUE,limit = 500)

Segment.Level	Segment.Parent	Segment.Child	n	Cell.ID	Quant.Error	x	y	z
1	1	1	13	3	0.17	2.46	-1.71	0.08
1	1	2	10	1	0.11	-1.45	-2.62	-0.07
1	1	3	23	5	0.17	2.26	1.95	0.07
1	1	4	12	4	0.09	2.64	-1.40	0.03
1	1	5	14	6	0.13	1.83	2.37	0.03
1	1	6	27	2	0.23	1.99	-2.22	0.05

Now let’s check the compression summary for HVT (torus_mapB). The table below shows no of cells, no of cells having quantization error below threshold and percentage of cells having quantization error below threshold for each level.

mapB_compression_summary <- torus_mapB[[3]]$compression_summary %>%  dplyr::mutate_if(is.numeric, funs(round(.,4)))
compressionSummaryTable(mapB_compression_summary)

segmentLevel	noOfCells	noOfCellsBelowQuantizationError	percentOfCellsBelowQuantizationErrorThreshold	parameters
1	6	5	0.83	n_cells: 6 quant.err: 0.2 distance_metric: L1_Norm error_metric: max quant_method: kmeans

5 Map C : Compressed Map without Novelty

Let us try to visualize the compressed Map C from the flow diagram below.

Figure 13:Data Segregation with highlighted bounding box in red around compressed map C

5.0.1 Iteration 1:

With the Novelties removed, we construct another hierarchical Voronoi tessellation map C layer 2 on the dataset without Novelty (containing 4983 records) and below mentioned model parameters.

Model Parameters

Number of Cells at each Level = 10
Maximum Depth = 2
Quantization Error Threshold = 0.2
Error Metric = Max
Distance Metric = Manhattan

torus_mapC <- list()
mapA_scale_summary = torus_mapA[[3]]$scale_summary
torus_mapC <- trainHVT(data_without_novelty,
                  n_cells = 10,
                  depth = 2,
                  quant.err = 0.2,
                  projection.scale = 10,
                  normalize = FALSE,
                  distance_metric = "L1_Norm",
                  error_metric = "max",
                  quant_method = "kmeans",
                  diagnose = FALSE,
                  scale_summary = mapA_scale_summary)

Now let’s check the compression summary for HVT (torus_mapC) where n_cell was set to 10. The table below shows no of cells, no of cells having quantization error below threshold and percentage of cells having quantization error below threshold for each level.

mapC_compression_summary <- torus_mapC[[3]]$compression_summary %>%  dplyr::mutate_if(is.numeric, funs(round(.,4)))
compressionSummaryTable(mapC_compression_summary)

segmentLevel	noOfCells	noOfCellsBelowQuantizationError	percentOfCellsBelowQuantizationErrorThreshold	parameters
1	10	0	0	n_cells: 10 quant.err: 0.2 distance_metric: L1_Norm error_metric: max quant_method: kmeans
2	100	0	0	n_cells: 10 quant.err: 0.2 distance_metric: L1_Norm error_metric: max quant_method: kmeans

As it can be seen from the table above, 0% of the cells have hit the quantization threshold error in level 1 and 0% of the cells have hit the quantization threshold error in level 2

5.0.2 Iteration 2:

Since, we are yet to achive atleast 80% compression at depth 2. Let’s try to compress again using the below mentioned set of model parameters and the dataset without novelty (containing 9501 records).

Model Parameters

Number of Cells at each Level = 23
Maximum Depth = 2
Quantization Error Threshold = 0.2
Error Metric = Max
Distance Metric = Manhattan

torus_mapC <- list()
torus_mapC <- trainHVT(data_without_novelty,
                  n_cells = 20,    
                  depth = 2,
                  quant.err = 0.2,
                  projection.scale = 10,
                  normalize = FALSE,
                  distance_metric = "L1_Norm",
                  error_metric = "max",
                  quant_method = "kmeans",
                  diagnose = FALSE,
                  scale_summary = mapA_scale_summary)

The datatable displayed below is the summary from map C (layer2). showing Cell.ID, Centroids and Quantization Error for each of the 367 cells.

summaryTable(torus_mapC[[3]]$summary,scroll = TRUE,limit = 500)

Segment.Level	Segment.Parent	Segment.Child	n	Cell.ID	Quant.Error	x	y	z
1	1	1	412	330	0.62	2.22	0.95	-0.69
1	1	2	452	51	0.66	-2.27	0.05	-0.73
1	1	3	404	193	0.64	0.81	-2.51	-0.35
1	1	4	490	144	0.58	-0.21	-1.52	0.78
1	1	5	363	340	0.59	2.67	-0.13	0.41
1	1	6	578	197	0.66	-0.20	1.39	0.70
1	1	7	489	35	0.69	-2.12	-0.97	0.71
1	1	8	587	240	0.65	0.65	1.01	-0.52
1	1	9	394	264	0.71	1.49	-1.51	0.83
1	1	10	431	67	0.74	-1.48	-1.30	-0.85
1	1	11	571	173	0.68	0.10	-1.14	-0.46
1	1	12	566	249	0.58	1.08	-0.12	0.32
1	1	13	482	76	0.64	-2.16	1.18	0.58
1	1	14	504	153	0.64	-1.00	1.42	-0.82
1	1	15	439	307	0.63	1.58	1.35	0.84
1	1	16	422	293	0.68	0.72	2.55	-0.27
1	1	17	488	283	0.72	1.78	-0.93	-0.81
1	1	18	362	46	0.64	-1.04	-2.55	0.06
1	1	19	718	127	0.56	-1.03	0.01	0.17
1	1	20	349	161	0.64	-1.03	2.53	0.23
2	1	1	32	335	0.16	2.42	0.67	-0.85
2	1	2	13	366	0.09	2.73	1.19	-0.16
2	1	3	17	365	0.12	2.81	1.03	0.07
2	1	4	27	317	0.14	1.95	0.83	-0.99
2	1	5	14	360	0.14	2.89	0.55	-0.30
2	1	6	29	296	0.13	1.53	0.87	-0.97
2	1	7	40	338	0.17	2.27	1.22	-0.80
2	1	8	17	306	0.11	1.91	0.23	-0.99
2	1	9	18	367	0.15	2.64	1.39	0.11
2	1	10	23	356	0.2	2.13	1.95	-0.43
2	1	11	21	342	0.17	2.63	0.12	-0.76
2	1	12	31	318	0.17	1.69	1.51	-0.95
2	1	13	32	294	0.16	1.61	0.42	-0.93
2	1	14	16	358	0.15	2.73	0.98	-0.41
2	1	15	18	362	0.16	2.53	1.45	-0.37
2	1	16	16	351	0.13	2.73	0.54	-0.61
2	1	17	27	328	0.14	2.32	0.24	-0.94
2	1	18	21	339	0.2	1.93	1.79	-0.76
2	1	19	0	NA	NA	NA	NA	NA
2	1	20	0	NA	NA	NA	NA	NA
2	2	1	23	52	0.17	-2.51	1.06	-0.67
2	2	2	13	45	0.13	-2.38	0.13	-0.91
2	2	3	30	58	0.12	-1.92	-0.41	-0.99
2	2	4	17	14	0.13	-2.65	-0.91	-0.57
2	2	5	19	18	0.14	-2.92	0.07	-0.37
2	2	6	16	9	0.18	-2.94	-0.48	-0.13
2	2	7	15	26	0.14	-2.86	0.62	-0.34
2	2	8	31	85	0.14	-1.52	-0.23	-0.88
2	2	9	25	24	0.14	-2.67	-0.25	-0.72
2	2	10	16	74	0.15	-2.11	0.95	-0.94
2	2	11	21	55	0.15	-2.30	0.60	-0.92
2	2	12	26	63	0.11	-2.00	0.14	-1.00
2	2	13	23	17	0.17	-2.98	0.10	0.06
2	2	14	24	31	0.14	-2.67	0.36	-0.70
2	2	15	15	42	0.1	-2.28	-0.27	-0.95
2	2	16	36	89	0.15	-1.73	0.54	-0.97
2	2	17	26	100	0.11	-1.40	0.15	-0.81
2	2	18	28	15	0.12	-2.80	-0.56	-0.50
2	2	19	26	86	0.11	-1.62	0.12	-0.92
2	2	20	22	28	0.12	-2.41	-0.66	-0.86
2	3	1	22	188	0.15	0.77	-2.87	0.17
2	3	2	29	177	0.17	0.52	-2.47	-0.84
2	3	3	33	280	0.17	1.74	-2.24	-0.51
2	3	4	22	160	0.15	0.36	-2.76	0.60
2	3	5	24	170	0.12	0.34	-2.11	-0.98
2	3	6	26	196	0.16	0.82	-2.58	0.69
2	3	7	20	138	0.18	0.23	-2.96	0.18
2	3	8	18	178	0.2	0.58	-2.81	-0.46
2	3	9	27	133	0.18	0.08	-2.85	-0.50
2	3	10	25	132	0.17	-0.02	-2.43	-0.89
2	3	11	36	251	0.19	1.36	-2.60	0.31
2	3	12	27	207	0.15	0.89	-1.94	-0.98
2	3	13	34	214	0.16	1.04	-2.48	-0.71
2	3	14	19	208	0.13	0.98	-2.77	-0.32
2	3	15	23	235	0.12	1.29	-2.07	-0.89
2	3	16	19	252	0.17	1.38	-2.60	-0.25
2	3	17	0	NA	NA	NA	NA	NA
2	3	18	0	NA	NA	NA	NA	NA
2	3	19	0	NA	NA	NA	NA	NA
2	3	20	0	NA	NA	NA	NA	NA
2	4	1	49	143	0.16	-0.29	-1.30	0.74
2	4	2	35	163	0.13	-0.08	-1.09	0.41
2	4	3	27	147	0.13	0.06	-2.09	0.99
2	4	4	42	97	0.17	-0.87	-1.34	0.91
2	4	5	33	142	0.12	-0.43	-0.97	0.34
2	4	6	35	187	0.16	0.45	-1.39	0.84
2	4	7	32	110	0.16	-0.40	-1.79	0.98
2	4	8	32	155	0.14	-0.01	-1.62	0.92
2	4	9	38	71	0.17	-1.00	-1.80	0.99
2	4	10	30	145	0.2	0.14	-2.48	0.86
2	4	11	16	96	0.18	-0.41	-2.31	0.92
2	4	12	40	183	0.17	0.44	-1.80	0.98
2	4	13	43	119	0.18	-0.71	-1.00	0.63
2	4	14	38	184	0.17	0.31	-1.16	0.60
2	4	15	0	NA	NA	NA	NA	NA
2	4	16	0	NA	NA	NA	NA	NA
2	4	17	0	NA	NA	NA	NA	NA
2	4	18	0	NA	NA	NA	NA	NA
2	4	19	0	NA	NA	NA	NA	NA
2	4	20	0	NA	NA	NA	NA	NA
2	5	1	18	312	0.12	1.98	0.01	0.99
2	5	2	17	361	0.16	2.78	0.85	0.41
2	5	3	19	325	0.17	2.40	-0.72	0.85
2	5	4	22	333	0.11	2.48	-0.17	0.86
2	5	5	18	314	0.11	2.13	-0.43	0.98
2	5	6	22	346	0.15	2.84	-0.74	0.31
2	5	7	16	344	0.15	2.73	-0.49	0.63
2	5	8	27	347	0.18	2.87	-0.20	-0.45
2	5	9	25	354	0.15	2.94	-0.12	0.30
2	5	10	15	357	0.14	2.96	0.19	-0.21
2	5	11	21	329	0.14	2.21	0.34	0.96
2	5	12	14	364	0.11	2.93	0.61	0.05
2	5	13	23	341	0.17	2.83	-0.89	-0.19
2	5	14	25	348	0.15	2.67	0.19	0.72
2	5	15	24	359	0.12	2.91	0.37	0.33
2	5	16	19	334	0.16	2.70	-1.13	0.33
2	5	17	20	349	0.13	2.56	0.61	0.77
2	5	18	18	352	0.15	2.96	-0.41	0.01
2	5	19	0	NA	NA	NA	NA	NA
2	5	20	0	NA	NA	NA	NA	NA
2	6	1	38	216	0.16	-0.05	1.70	0.95
2	6	2	41	182	0.15	-0.39	0.92	0.05
2	6	3	46	238	0.17	0.52	1.11	0.62
2	6	4	40	254	0.14	0.46	1.56	0.92
2	6	5	39	218	0.16	0.12	1.30	0.71
2	6	6	35	171	0.12	-0.78	1.76	0.99
2	6	7	38	175	0.16	-0.57	0.93	0.43
2	6	8	36	203	0.16	-0.33	2.10	0.98
2	6	9	41	150	0.15	-1.04	1.38	0.95
2	6	10	30	195	0.1	-0.12	1.00	0.14
2	6	11	40	157	0.17	-0.87	1.03	0.75
2	6	12	36	213	0.14	0.15	1.05	0.35
2	6	13	28	268	0.14	0.47	2.05	0.98
2	6	14	34	185	0.15	-0.45	1.51	0.90
2	6	15	34	191	0.14	-0.24	1.17	0.59
2	6	16	22	245	0.15	0.14	2.29	0.94
2	6	17	0	NA	NA	NA	NA	NA
2	6	18	0	NA	NA	NA	NA	NA
2	6	19	0	NA	NA	NA	NA	NA
2	6	20	0	NA	NA	NA	NA	NA
2	7	1	31	2	0.21	-2.60	-1.47	-0.02
2	7	2	20	16	0.14	-2.82	-0.20	0.54
2	7	3	24	30	0.17	-2.47	-0.12	0.87
2	7	4	17	36	0.13	-2.18	-0.57	0.96
2	7	5	22	4	0.15	-2.81	-1.00	0.06
2	7	6	18	1	0.16	-2.25	-1.94	0.17
2	7	7	28	49	0.12	-1.78	-0.95	0.99
2	7	8	20	8	0.14	-2.86	-0.60	0.36
2	7	9	25	6	0.18	-2.55	-1.29	0.49
2	7	10	33	57	0.12	-1.47	-1.34	0.99
2	7	11	20	33	0.13	-1.64	-1.75	0.91
2	7	12	22	20	0.12	-2.55	-0.47	0.80
2	7	13	23	77	0.12	-1.52	-0.60	0.92
2	7	14	22	54	0.11	-2.01	-0.05	0.99
2	7	15	36	59	0.16	-1.84	-0.41	0.99
2	7	16	18	5	0.13	-2.29	-1.71	0.50
2	7	17	34	22	0.15	-2.06	-1.41	0.85
2	7	18	13	11	0.15	-1.96	-1.94	0.64
2	7	19	32	82	0.12	-1.25	-0.98	0.91
2	7	20	31	19	0.13	-2.34	-0.99	0.83
2	8	1	29	219	0.1	0.27	0.97	0.05
2	8	2	35	242	0.12	0.70	0.91	-0.52
2	8	3	35	237	0.12	0.69	0.77	-0.23
2	8	4	30	253	0.13	0.94	0.48	-0.34
2	8	5	28	212	0.14	0.11	1.13	-0.50
2	8	6	18	241	0.1	0.79	0.61	0.02
2	8	7	36	199	0.15	-0.07	1.02	-0.22
2	8	8	48	226	0.13	0.39	1.13	-0.59
2	8	9	35	257	0.14	0.62	1.45	-0.90
2	8	10	18	239	0.14	0.33	1.76	-0.97
2	8	11	24	217	0.12	0.11	1.39	-0.79
2	8	12	23	289	0.16	1.24	1.16	-0.94
2	8	13	39	287	0.15	0.99	1.63	-0.99
2	8	14	33	266	0.14	1.21	0.38	-0.67
2	8	15	28	224	0.12	0.43	0.93	-0.23
2	8	16	25	261	0.1	0.98	0.70	-0.61
2	8	17	29	274	0.11	1.25	0.78	-0.85
2	8	18	36	230	0.14	0.58	0.84	0.21
2	8	19	38	263	0.14	0.88	1.14	-0.82
2	8	20	0	NA	NA	NA	NA	NA
2	9	1	38	247	0.14	1.27	-1.35	0.98
2	9	2	19	321	0.2	2.37	-1.76	0.27
2	9	3	29	206	0.15	0.77	-1.56	0.95
2	9	4	31	275	0.17	1.67	-1.81	0.88
2	9	5	29	276	0.13	1.64	-1.12	0.99
2	9	6	30	305	0.17	2.11	-1.20	0.89
2	9	7	36	288	0.17	1.66	-0.77	0.97
2	9	8	48	220	0.19	0.92	-1.06	0.80
2	9	9	26	303	0.15	2.04	-1.87	0.62
2	9	10	20	319	0.2	2.35	-1.49	0.61
2	9	11	30	225	0.13	1.10	-1.83	0.98
2	9	12	15	232	0.14	1.24	-2.30	0.77
2	9	13	22	202	0.17	0.79	-2.19	0.93
2	9	14	21	272	0.16	1.63	-2.30	0.55
2	9	15	0	NA	NA	NA	NA	NA
2	9	16	0	NA	NA	NA	NA	NA
2	9	17	0	NA	NA	NA	NA	NA
2	9	18	0	NA	NA	NA	NA	NA
2	9	19	0	NA	NA	NA	NA	NA
2	9	20	0	NA	NA	NA	NA	NA
2	10	1	32	75	0.12	-1.34	-1.19	-0.97
2	10	2	21	95	0.11	-1.15	-0.87	-0.83
2	10	3	25	69	0.13	-1.56	-0.93	-0.97
2	10	4	20	48	0.11	-1.91	-0.85	-0.99
2	10	5	16	111	0.12	-0.86	-0.85	-0.61
2	10	6	21	7	0.18	-2.08	-1.97	-0.46
2	10	7	11	90	0.09	-0.62	-1.92	-0.99
2	10	8	26	10	0.19	-2.29	-1.65	-0.54
2	10	9	31	62	0.14	-1.31	-1.62	-0.99
2	10	10	23	106	0.1	-1.10	-0.62	-0.67
2	10	11	31	40	0.17	-1.87	-1.28	-0.95
2	10	12	17	88	0.1	-1.37	-0.54	-0.85
2	10	13	14	70	0.09	-1.66	-0.58	-0.97
2	10	14	31	104	0.13	-0.86	-1.20	-0.85
2	10	15	25	29	0.16	-1.79	-1.79	-0.83
2	10	16	29	21	0.17	-2.30	-1.13	-0.81
2	10	17	14	39	0.18	-1.41	-2.08	-0.85
2	10	18	22	68	0.12	-0.99	-1.99	-0.97
2	10	19	22	93	0.13	-0.82	-1.53	-0.96
2	10	20	0	NA	NA	NA	NA	NA
2	11	1	56	162	0.17	-0.08	-1.08	-0.40
2	11	2	75	186	0.18	0.34	-0.94	0.11
2	11	3	46	190	0.16	0.44	-0.96	-0.34
2	11	4	33	205	0.12	0.69	-1.09	-0.70
2	11	5	65	151	0.18	-0.31	-0.94	0.01
2	11	6	27	118	0.15	-0.32	-1.80	-0.97
2	11	7	31	164	0.16	0.17	-1.75	-0.96
2	11	8	32	201	0.15	0.71	-1.47	-0.92
2	11	9	39	154	0.16	-0.07	-1.37	-0.77
2	11	10	41	180	0.15	0.31	-1.25	-0.70
2	11	11	41	211	0.13	0.75	-0.83	-0.46
2	11	12	56	136	0.17	-0.58	-0.91	-0.39
2	11	13	29	125	0.16	-0.49	-1.29	-0.77
2	11	14	0	NA	NA	NA	NA	NA
2	11	15	0	NA	NA	NA	NA	NA
2	11	16	0	NA	NA	NA	NA	NA
2	11	17	0	NA	NA	NA	NA	NA
2	11	18	0	NA	NA	NA	NA	NA
2	11	19	0	NA	NA	NA	NA	NA
2	11	20	0	NA	NA	NA	NA	NA
2	12	1	60	260	0.2	1.13	0.11	0.49
2	12	2	45	278	0.17	1.50	-0.37	0.88
2	12	3	51	256	0.13	0.94	0.57	0.43
2	12	4	40	246	0.14	1.02	0.01	-0.21
2	12	5	29	273	0.15	1.28	0.38	0.74
2	12	6	34	221	0.11	0.87	-0.58	0.29
2	12	7	32	210	0.13	0.73	-0.86	0.49
2	12	8	19	233	0.13	1.02	-0.38	-0.41
2	12	9	27	222	0.13	0.87	-0.53	-0.19
2	12	10	54	244	0.18	1.12	-0.51	0.64
2	12	11	31	255	0.17	1.15	-0.05	-0.54
2	12	12	37	292	0.2	1.56	0.07	0.89
2	12	13	34	236	0.13	0.99	-0.25	0.20
2	12	14	18	215	0.11	0.74	-0.68	0.03
2	12	15	55	250	0.15	0.95	0.31	0.07
2	12	16	0	NA	NA	NA	NA	NA
2	12	17	0	NA	NA	NA	NA	NA
2	12	18	0	NA	NA	NA	NA	NA
2	12	19	0	NA	NA	NA	NA	NA
2	12	20	0	NA	NA	NA	NA	NA
2	13	1	12	123	0.08	-1.37	1.31	0.99
2	13	2	24	81	0.16	-2.01	1.91	0.61
2	13	3	19	64	0.17	-2.30	1.53	0.62
2	13	4	36	61	0.22	-2.36	1.67	-0.42
2	13	5	24	25	0.19	-2.82	0.53	0.45
2	13	6	27	50	0.17	-2.38	0.61	0.88
2	13	7	34	73	0.13	-2.04	0.78	0.97
2	13	8	24	43	0.14	-2.69	1.11	0.39
2	13	9	20	120	0.13	-1.33	0.93	0.92
2	13	10	25	102	0.17	-1.68	1.78	0.88
2	13	11	26	105	0.12	-1.60	1.10	0.99
2	13	12	23	80	0.13	-2.00	1.19	0.93
2	13	13	23	103	0.11	-1.67	1.50	0.96
2	13	14	20	56	0.15	-2.42	1.06	0.76
2	13	15	20	32	0.22	-2.62	0.28	0.76
2	13	16	32	47	0.18	-2.56	1.54	0.08
2	13	17	16	60	0.14	-2.10	0.37	0.98
2	13	18	29	66	0.17	-2.21	1.99	0.09
2	13	19	26	38	0.25	-2.77	1.05	-0.18
2	13	20	22	94	0.13	-1.62	0.57	0.96
2	14	1	24	165	0.13	-0.73	0.84	-0.46
2	14	2	33	200	0.15	-0.37	2.14	-0.97
2	14	3	31	92	0.21	-1.84	1.93	-0.72
2	14	4	27	117	0.14	-1.39	0.85	-0.93
2	14	5	34	148	0.12	-1.09	1.50	-0.98
2	14	6	21	204	0.14	-0.18	1.67	-0.94
2	14	7	33	169	0.14	-0.71	1.19	-0.78
2	14	8	26	98	0.11	-1.69	1.11	-0.99
2	14	9	6	172	0.06	-0.58	0.84	-0.20
2	14	10	19	122	0.13	-1.25	0.61	-0.79
2	14	11	26	176	0.11	-0.83	2.29	-0.89
2	14	12	27	189	0.16	-0.32	1.22	-0.67
2	14	13	25	139	0.22	-1.30	2.07	-0.88
2	14	14	25	146	0.18	-1.04	1.05	-0.85
2	14	15	25	114	0.13	-1.49	1.51	-0.98
2	14	16	27	79	0.19	-2.08	1.46	-0.82
2	14	17	32	179	0.13	-0.54	1.54	-0.92
2	14	18	22	181	0.14	-0.44	0.97	-0.36
2	14	19	20	149	0.12	-0.94	0.76	-0.61
2	14	20	21	168	0.11	-0.83	1.81	-0.99
2	15	1	21	337	0.17	1.56	2.25	0.65
2	15	2	19	309	0.15	1.13	2.20	0.87
2	15	3	33	302	0.12	1.45	1.18	0.99
2	15	4	34	290	0.16	0.91	1.76	0.99
2	15	5	15	363	0.14	2.45	1.49	0.46
2	15	6	27	326	0.14	1.87	1.34	0.94
2	15	7	17	353	0.13	2.53	1.14	0.62
2	15	8	30	286	0.13	1.23	0.89	0.87
2	15	9	20	350	0.15	2.13	1.65	0.71
2	15	10	31	262	0.14	0.86	0.90	0.66
2	15	11	20	323	0.13	2.03	0.59	0.98
2	15	12	25	336	0.13	2.23	0.93	0.90
2	15	13	39	282	0.18	1.01	1.30	0.93
2	15	14	26	355	0.2	2.03	2.02	0.46
2	15	15	30	315	0.1	1.79	0.91	0.99
2	15	16	17	295	0.14	1.52	0.61	0.92
2	15	17	35	320	0.17	1.56	1.77	0.92
2	15	18	0	NA	NA	NA	NA	NA
2	15	19	0	NA	NA	NA	NA	NA
2	15	20	0	NA	NA	NA	NA	NA
2	16	1	23	297	0.15	0.92	2.18	-0.92
2	16	2	38	316	0.25	1.02	2.61	0.56
2	16	3	20	308	0.14	0.86	2.84	-0.22
2	16	4	35	285	0.2	0.44	2.62	0.74
2	16	5	14	299	0.15	0.55	2.93	0.16
2	16	6	19	304	0.14	1.24	2.00	-0.93
2	16	7	16	234	0.1	0.16	2.02	-1.00
2	16	8	18	343	0.15	1.53	2.51	0.28
2	16	9	17	228	0.1	-0.01	2.36	-0.93
2	16	10	26	331	0.2	1.19	2.73	-0.07
2	16	11	25	345	0.19	1.71	2.36	-0.37
2	16	12	20	227	0.15	-0.13	2.63	-0.77
2	16	13	21	271	0.14	0.24	2.86	0.47
2	16	14	12	243	0.12	-0.10	2.88	-0.45
2	16	15	27	300	0.16	0.75	2.62	-0.67
2	16	16	27	324	0.16	1.33	2.39	-0.67
2	16	17	15	279	0.15	0.29	2.93	-0.31
2	16	18	18	265	0.15	0.24	2.63	-0.75
2	16	19	19	270	0.11	0.52	2.20	-0.96
2	16	20	12	269	0.1	0.10	2.99	0.00
2	17	1	29	311	0.16	2.35	-1.00	-0.81
2	17	2	20	258	0.12	1.37	-1.05	-0.96
2	17	3	26	332	0.16	2.62	-1.27	-0.38
2	17	4	40	281	0.17	1.54	-0.07	-0.87
2	17	5	21	291	0.16	1.86	-1.92	-0.72
2	17	6	18	310	0.18	2.27	-1.88	-0.30
2	17	7	37	301	0.16	1.98	-0.51	-0.99
2	17	8	15	313	0.16	2.34	-1.61	-0.53
2	17	9	22	229	0.12	1.13	-1.21	-0.93
2	17	10	20	298	0.16	2.04	-1.46	-0.85
2	17	11	24	322	0.2	2.36	-0.26	-0.91
2	17	12	34	248	0.19	1.34	-1.60	-0.98
2	17	13	25	327	0.17	2.58	-0.75	-0.70
2	17	14	26	284	0.11	1.72	-0.87	-0.99
2	17	15	29	267	0.15	1.47	-0.61	-0.91
2	17	16	35	259	0.15	1.29	-0.34	-0.74
2	17	17	38	231	0.13	1.07	-0.72	-0.70
2	17	18	29	277	0.13	1.74	-1.31	-0.98
2	17	19	0	NA	NA	NA	NA	NA
2	17	20	0	NA	NA	NA	NA	NA
2	18	1	30	78	0.15	-0.33	-2.97	0.03
2	18	2	18	41	0.17	-1.19	-2.39	-0.73
2	18	3	23	72	0.17	-0.70	-2.39	-0.85
2	18	4	30	65	0.19	-0.73	-2.47	0.80
2	18	5	22	13	0.15	-1.70	-2.39	-0.33
2	18	6	33	84	0.2	-0.29	-2.82	0.52
2	18	7	13	87	0.18	-0.34	-2.70	-0.67
2	18	8	22	3	0.14	-2.04	-2.18	0.00
2	18	9	28	23	0.17	-1.31	-2.57	0.43
2	18	10	20	44	0.13	-0.88	-2.81	0.30
2	18	11	30	34	0.17	-1.36	-2.15	0.82
2	18	12	19	37	0.16	-0.97	-2.82	-0.14
2	18	13	22	53	0.17	-0.74	-2.75	-0.51
2	18	14	27	12	0.18	-1.75	-2.29	0.43
2	18	15	25	27	0.15	-1.28	-2.60	-0.42
2	18	16	0	NA	NA	NA	NA	NA
2	18	17	0	NA	NA	NA	NA	NA
2	18	18	0	NA	NA	NA	NA	NA
2	18	19	0	NA	NA	NA	NA	NA
2	18	20	0	NA	NA	NA	NA	NA
2	19	1	44	116	0.14	-1.06	-0.27	0.42
2	19	2	45	137	0.17	-1.07	0.60	0.63
2	19	3	26	115	0.13	-0.96	-0.51	-0.41
2	19	4	28	129	0.13	-0.76	-0.66	-0.07
2	19	5	46	131	0.11	-1.04	0.10	0.29
2	19	6	38	140	0.13	-0.95	0.31	-0.09
2	19	7	30	99	0.14	-1.18	-0.53	0.71
2	19	8	37	141	0.15	-0.95	0.41	0.26
2	19	9	29	126	0.09	-0.99	-0.13	0.05
2	19	10	36	124	0.11	-0.91	-0.42	-0.02
2	19	11	55	130	0.18	-1.10	0.29	-0.50
2	19	12	36	101	0.24	-1.44	0.32	0.84
2	19	13	36	91	0.19	-1.42	-0.18	0.82
2	19	14	39	159	0.18	-0.76	0.69	0.21
2	19	15	34	108	0.16	-1.20	-0.15	-0.62
2	19	16	40	112	0.12	-1.20	0.08	0.60
2	19	17	23	113	0.13	-0.91	-0.71	0.52
2	19	18	31	134	0.1	-0.72	-0.73	0.23
2	19	19	30	121	0.13	-1.04	-0.15	-0.32
2	19	20	35	156	0.15	-0.80	0.63	-0.21
2	20	1	16	194	0.15	-0.49	2.46	0.85
2	20	2	27	166	0.16	-1.01	2.57	-0.62
2	20	3	25	192	0.17	-0.67	2.90	-0.08
2	20	4	27	152	0.18	-1.19	2.72	-0.14
2	20	5	24	109	0.16	-1.54	2.26	0.66
2	20	6	25	198	0.16	-0.55	2.73	-0.61
2	20	7	18	83	0.16	-1.93	2.26	0.15
2	20	8	29	174	0.15	-0.92	2.71	0.49
2	20	9	20	135	0.09	-1.33	1.95	0.93
2	20	10	22	223	0.17	-0.17	2.66	0.73
2	20	11	28	107	0.19	-1.69	2.36	-0.39
2	20	12	16	158	0.09	-1.01	2.12	0.94
2	20	13	21	167	0.14	-0.95	2.40	0.80
2	20	14	30	128	0.17	-1.42	2.56	0.35
2	20	15	21	209	0.18	-0.42	2.91	0.30
2	20	16	0	NA	NA	NA	NA	NA
2	20	17	0	NA	NA	NA	NA	NA
2	20	18	0	NA	NA	NA	NA	NA
2	20	19	0	NA	NA	NA	NA	NA
2	20	20	0	NA	NA	NA	NA	NA

Now let’s check the compression summary for HVT (torus_mapC). The table below shows no of cells, no of cells having quantization error below threshold and percentage of cells having quantization error below threshold for each level.

mapC_compression_summary <- torus_mapC[[3]]$compression_summary %>%  dplyr::mutate_if(is.numeric, funs(round(.,4)))
compressionSummaryTable(mapC_compression_summary)

segmentLevel	noOfCells	noOfCellsBelowQuantizationError	percentOfCellsBelowQuantizationErrorThreshold	parameters
1	20	0	0	n_cells: 20 quant.err: 0.2 distance_metric: L1_Norm error_metric: max quant_method: kmeans
2	347	338	0.97	n_cells: 20 quant.err: 0.2 distance_metric: L1_Norm error_metric: max quant_method: kmeans

As it can be seen from the table above, 0% of the cells have hit the quantization threshold error in level 1 and 97% of the cells have hit the quantization threshold error in level 2

Let’s plot the Voronoi tessellation for layer 2 (map C)

plotHVT(torus_mapC,
        line.width = c(0.4,0.2), 
        color.vec = c("#141B41","#0582CA"),
        centroid.size = 0.1,
        maxDepth = 2, 
        heatmap = '2DHVT')

Figure 14: The Voronoi Tessellation for layer 2 (map C) shown for the 347 cells in the dataset ’torus’ at level 2

Heat Maps

Now let’s plot all the features for each cell at level two as a heatmap for better visualization.

The heatmaps displayed below provides a visual representation of the spatial characteristics of the computers data, allowing us to observe patterns and trends in the distribution of each of the features (x,y,z). The sheer green shades highlight regions with higher values in each of the heatmaps, while the indigo shades indicate areas with the lowest values in each of the heatmaps. By analyzing these heatmaps, we can gain insights into the variations and relationships between each of these features within the computers data.


  plotHVT(
  torus_mapC,
  traindata,
  child.level = 2,
  hmap.cols = "x",
  line.width = c(0.6,0.4),
  color.vec = c("#141B41","#0582CA"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = TRUE,
  quant.error.hmap = 0.2,
  n_cells.hmap = 100,
  heatmap = '2DHEATMAP'
)

Figure 15: The Voronoi Tessellation with the heat map overlaid for feature x in the ’torus’ dataset


  plotHVT(
  torus_mapC,
  traindata,
  child.level = 2,
  hmap.cols = "y",
  line.width = c(0.6,0.4),
  color.vec = c("#141B41","#0582CA"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = TRUE,
  quant.error.hmap = 0.2,
  n_cells.hmap = 100,
  heatmap = '2DHEATMAP'
)

Figure 16: The Voronoi Tessellation with the heat map overlaid for features y in the ’torus’ dataset


  plotHVT(
  torus_mapC,
  traindata,
  child.level = 2,
  hmap.cols = "z",
  line.width = c(0.6,0.4),
  color.vec = c("#141B41","#0582CA"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = TRUE,
  quant.error.hmap = 0.2,
  n_cells.hmap = 100,
  heatmap = '2DHEATMAP'
)

Figure 17: The Voronoi Tessellation with the heat map overlaid for features z in the ’torus’ dataset

We now have the set of maps (map A, map B & map C) which will be used to score, which map and cell each test record is assigned to, but before that lets view our test dataset

6 Scoring on Test Data

Now once we have built the model, let us try to score using our test dataset (containing 2400 data points) which cell and which layer each point belongs to.

Testing Dataset

The testing dataset includes the following columns:

x: This column represents the X-coordinate of each point in the torus.
y: This column represents the Y-coordinate of each point in the torus.
z: This column represents the Z-coordinate of each point in the torus.

Let’s have a look at our randomly selected test dataset containing 2400 datapoints.

Table(head(testdata))

x	y	z
-1.0308	1.1066	-0.8731
1.8847	0.1895	0.9944
-1.0046	-1.8170	-0.9971
-2.4446	-1.6528	0.3097
-0.3961	-2.1775	0.9770
-1.1130	-0.6516	-0.7040

The scoreLayeredHVT function is used to score the test data using the scored set of maps. This function takes an input - a test data and a set of maps (map A, map B, map C).

Now, Let us understand the scoreLayeredHVT function.

scoreLayeredHVT(data,
                map_A,
                map_B,
                map_C,
                mad.threshold = 0.2,
                normalize = TRUE, 
                distance_metric="L1_Norm",
                error_metric="max",
                child.level = 1, 
                line.width = c(0.6, 0.4, 0.2),
                color.vec = c("#141B41", "#6369D1", "#D8D2E1"),
                yVar= NULL,
                ...)

Each of the parameters of scoreLayeredHVT function has been explained below:

data - A dataframe containing the test dataset. The dataframe should have all the variable(features) used for training.
map A - Result (hvt.result) obtained from HVT function while performing hierarchical vector quantization on train data. This list containes information about the hierarchical vector quantized data along with a summary section.
map B - Result (hvt.result) obtained from HVT function while performing hierarchical vector quantization on novelty data. Novelty data is a subset of the training data obtained as a result of removeNovelty function (1st element).
map C - Result (hvt.result) obtained from HVT function while performing hierarchical vector quantization on training data without novelty. This data is a subset of the training data obtained as a result of removeNovelty function (2nd element).
child.level - A number indicating the depth for which the heat map is to be plotted (Only used if hmap.cols is not NULL), Each depth represents a different level of clustering or partitioning of the data.
mad.threshold - A threshold value used to filter data based on the Median Absolute Deviation (MAD) of the Quant.Error variable. It determines how extreme a deviation from the median has to be in order to consider as novelty
normalize - A logical value indicating if the dataset should be normalized. When set to TRUE, scales the values of all features to have a mean of 0 and a standard deviation of 1 (Z-score)
distance_metric - The distance metric can be L1_Norm(Manhattan) or L2_Norm(Eucledian). L1_Norm is selected by default. The distance metric is used to calculate the distance between an n dimensional point and centroid. The distance metric can be different from the one used during training.
error_metric - The error metric can be mean or max. max is selected by default. max will return the max of m values and mean will take mean of m values where each value is a distance between a point and centroid of the cell. The error metric can be different from the one used during training.
yVar - A character or a vector representing the name of the dependent variable(s)
line.width - A vector indicating the line widths of the tessellation boundaries for each layer. (Optional Parameters)
color.vec - A vector indicating the colors of the tessellations boundaries at each layer. (Optional Parameters)

The function predicts based on the HVT maps - map A, map B and map C, constructed using trainHVT function. For each test record, the function will assign that record to Layer1 or Layer2. Layer1 contains the cell ids from map A and Layer 2 contains cell ids from map B (novelty map) and map C (map without novelty).

Scoring Algorithm

The prediction algorithm recursively calculates the distance between each point in the test dataset and the cell centroids for each level. The following steps explain the scoring method for a single point in the test dataset:

Calculate the distance between the point and the centroid of all the cells in the first level.
Find the cell whose centroid has minimum distance to the point.
Check if the cell drills down further to form more cells.
If it doesn’t, return the path. Or else repeat steps 1 to 4 till we reach a level at which the cell doesn’t drill down further.

Note : The Scoring algorithm will not work if some of the variables used to perform quantization are missing. In the test dataset, we should not remove any features


validation_data <- testdata
new_predict <- scoreLayeredHVT(
    data=validation_data,
    torus_mapA,
    torus_mapB,
    torus_mapC,
    normalize = TRUE
  )

Let’s see which cell and layer each point belongs to and check the Mean Absolute Difference for each of the 2400 records.


act_pred <- new_predict[["actual_predictedTable"]]
rownames(act_pred) <- NULL
act_pred %>% head(1000) %>%as.data.frame() %>%Table(scroll = TRUE)

Row.Number	act_x	act_y	act_z	Layer1.Cell.ID	Layer2.Cell.ID	pred_x	pred_y	pred_z	diff
1	-1.0308	1.1066	-0.8731	A650	C153	-1.0030224	1.4214296	-0.8194117	0.1320985
2	1.8847	0.1895	0.9944	A470	C307	1.5763323	1.3461567	0.8384533	0.5403237
3	-1.0046	-1.8170	-0.9971	A138	C67	-1.4757775	-1.2955060	-0.8486053	0.3803887
4	-2.4446	-1.6528	0.3097	A94	C35	-2.1242339	-0.9715258	0.7096658	0.4672020
5	-0.3961	-2.1775	0.9770	A112	C144	-0.2145520	-1.5164273	0.7835631	0.3453525
6	-1.1130	-0.6516	-0.7040	A373	C67	-1.4757775	-1.2955060	-0.8486053	0.3837630
7	0.7520	-2.6044	0.7034	A56	C193	0.8084450	-2.5111158	-0.3496015	0.4009102
8	2.0288	1.9519	0.5790	A802	C307	1.5763323	1.3461567	0.8384533	0.4392214
9	0.7930	2.4428	0.8228	A831	C293	0.7212818	2.5491813	-0.2728450	0.4245815
10	-0.0373	-2.8690	-0.4944	A25	C193	0.8084450	-2.5111158	-0.3496015	0.4494759
11	1.6664	-2.1227	-0.7155	A65	C283	1.7808158	-0.9337703	-0.8105779	0.4661411
12	-0.2545	-1.6160	-0.9314	A163	C173	0.0988042	-1.1378972	-0.4550217	0.4359284
13	2.3377	-0.4287	-0.9263	A290	C283	1.7808158	-0.9337703	-0.8105779	0.3925589
14	1.4772	-0.5194	-0.9008	A348	C283	1.7808158	-0.9337703	-0.8105779	0.2694027
15	-0.4677	1.6539	0.9596	A756	C197	-0.1968420	1.3899623	0.6958189	0.2661923
16	1.1034	-0.7534	-0.7478	A294	C283	1.7808158	-0.9337703	-0.8105779	0.3068546
17	2.0890	-0.6341	-0.9831	A231	C283	1.7808158	-0.9337703	-0.8105779	0.2601255
18	-1.6832	-0.2035	0.9525	A464	C35	-2.1242339	-0.9715258	0.7096658	0.4839646
19	-0.3870	1.0347	0.4455	A622	C197	-0.1968420	1.3899623	0.6958189	0.2652464
20	-0.8512	2.8363	-0.2755	A894	C161	-1.0348261	2.5280129	0.2324966	0.3333032
21	2.2895	-0.4637	0.9419	A300	C340	2.6666782	-0.1317501	0.4147766	0.4120838
22	-2.0314	-0.2369	-0.9990	A422	C51	-2.2655670	0.0495469	-0.7279562	0.2638859
23	-0.5293	-0.8566	0.1173	A341	C127	-1.0331492	0.0055723	0.1700299	0.4729171
24	-1.8571	1.6274	-0.8830	A822	C153	-1.0030224	1.4214296	-0.8194117	0.3745454
25	-0.8999	0.4451	0.0885	A533	C127	-1.0331492	0.0055723	0.1700299	0.2181023
26	0.7219	2.8642	0.3005	A872	C293	0.7212818	2.5491813	-0.2728450	0.2963273
27	0.7150	-0.7791	-0.3341	A328	C173	0.0988042	-1.1378972	-0.4550217	0.3653049
28	-2.9876	-0.2310	0.0831	A454	C51	-2.2655670	0.0495469	-0.7279562	0.6045454
29	2.9383	0.6049	0.0126	A578	C340	2.6666782	-0.1317501	0.4147766	0.4701495
30	2.5807	-1.3975	-0.3553	A85	C283	1.7808158	-0.9337703	-0.8105779	0.5729639
31	1.6829	-2.0223	0.7758	A87	C264	1.4868170	-1.5149655	0.8303546	0.2526574
32	-0.3810	1.7125	-0.9694	A737	C153	-1.0030224	1.4214296	-0.8194117	0.3543604
33	1.0605	1.2803	0.9413	A660	C307	1.5763323	1.3461567	0.8384533	0.2281786
34	0.2569	1.4850	0.8701	A703	C197	-0.1968420	1.3899623	0.6958189	0.2410203
35	1.1535	1.3623	-0.9766	A655	C240	0.6514734	1.0103327	-0.5200428	0.4368504
36	0.5354	1.8832	0.9991	A753	C197	-0.1968420	1.3899623	0.6958189	0.5095870
37	-1.5746	-0.0465	0.9053	A464	C127	-1.0331492	0.0055723	0.1700299	0.4429311
38	-0.9720	-1.2693	0.9160	A223	C144	-0.2145520	-1.5164273	0.7835631	0.3790041
39	-1.5215	1.8082	0.9317	A809	C76	-2.1614253	1.1751861	0.5762133	0.5428086
40	-0.7437	0.8610	0.5065	A584	C197	-0.1968420	1.3899623	0.6958189	0.4217130
41	0.4282	-1.0374	0.4791	A297	C173	0.0988042	-1.1378972	-0.4550217	0.4546716
42	2.4955	0.0918	0.8676	A458	C340	2.6666782	-0.1317501	0.4147766	0.2825173
43	-0.7473	-2.7938	0.4520	A39	C46	-1.0353834	-2.5511392	0.0634906	0.3064179
44	-0.8596	1.5771	-0.9790	A741	C153	-1.0030224	1.4214296	-0.8194117	0.1528937
45	1.0781	-2.6842	0.4509	A16	C193	0.8084450	-2.5111158	-0.3496015	0.4144135
46	0.7559	1.9550	0.9954	A765	C307	1.5763323	1.3461567	0.8384533	0.5287408
47	0.5300	1.3668	0.8455	A681	C197	-0.1968420	1.3899623	0.6958189	0.2998952
48	-2.9305	0.5814	0.1566	A683	C76	-2.1614253	1.1751861	0.5762133	0.5941580
49	2.3888	-1.0670	0.7875	A149	C264	1.4868170	-1.5149655	0.8303546	0.4642677
50	-0.6055	0.8773	-0.3572	A598	C153	-1.0030224	1.4214296	-0.8194117	0.4679546
51	0.7468	-1.9001	0.9991	A140	C264	1.4868170	-1.5149655	0.8303546	0.4312990
52	1.1944	-1.3305	-0.9773	A192	C283	1.7808158	-0.9337703	-0.8105779	0.3832892
53	0.9147	1.2969	-0.9108	A655	C240	0.6514734	1.0103327	-0.5200428	0.3135170
54	1.1413	1.0563	-0.8956	A602	C240	0.6514734	1.0103327	-0.5200428	0.3037837
55	-0.8597	-0.8383	0.6010	A355	C127	-1.0331492	0.0055723	0.1700299	0.4827638
56	1.4374	1.2279	0.9940	A714	C307	1.5763323	1.3461567	0.8384533	0.1375786
57	-1.5625	1.0275	0.9915	A708	C76	-2.1614253	1.1751861	0.5762133	0.3872994
58	-0.3022	-1.3611	0.7956	A216	C144	-0.2145520	-1.5164273	0.7835631	0.0850041
59	-0.7561	-2.5384	-0.7611	A71	C46	-1.0353834	-2.5511392	0.0634906	0.3722044
60	-1.6457	-2.1635	-0.6958	A93	C67	-1.4757775	-1.2955060	-0.8486053	0.3969073
61	-0.7163	-2.3849	-0.8716	A71	C46	-1.0353834	-2.5511392	0.0634906	0.4734711
62	-1.8574	-0.2955	0.9929	A427	C35	-2.1242339	-0.9715258	0.7096658	0.4086980
63	0.5359	1.3339	-0.8268	A656	C240	0.6514734	1.0103327	-0.5200428	0.2486327
64	0.2274	1.1488	0.5593	A640	C197	-0.1968420	1.3899623	0.6958189	0.2673077
65	1.0874	-0.1278	0.4251	A433	C249	1.0778184	-0.1223857	0.3159433	0.0413842
66	1.1080	2.7875	-0.0260	A877	C293	0.7212818	2.5491813	-0.2728450	0.2906273
67	-0.4462	2.1556	-0.9795	A795	C153	-1.0030224	1.4214296	-0.8194117	0.4836937
68	1.4935	2.5288	0.3496	A861	C293	0.7212818	2.5491813	-0.2728450	0.4716815
69	-2.2003	-1.7403	0.5929	A128	C35	-2.1242339	-0.9715258	0.7096658	0.3205354
70	0.3254	1.9173	0.9985	A764	C197	-0.1968420	1.3899623	0.6958189	0.4507536
71	-0.6653	-1.5250	0.9418	A207	C144	-0.2145520	-1.5164273	0.7835631	0.2058525
72	0.5849	-0.8531	-0.2598	A328	C173	0.0988042	-1.1378972	-0.4550217	0.3220382
73	-0.9395	2.6663	-0.5623	A880	C161	-1.0348261	2.5280129	0.2324966	0.3428032
74	-1.6866	2.1137	0.7101	A858	C161	-1.0348261	2.5280129	0.2324966	0.5145634
75	0.2761	-1.1245	0.5393	A258	C144	-0.2145520	-1.5164273	0.7835631	0.3756141
76	1.1576	1.0473	0.8985	A579	C307	1.5763323	1.3461567	0.8384533	0.2592119
77	1.0850	-1.6815	1.0000	A133	C264	1.4868170	-1.5149655	0.8303546	0.2459990
78	2.6678	-0.0291	-0.7442	A420	C340	2.6666782	-0.1317501	0.4147766	0.4209162
79	-0.5183	1.0593	-0.5713	A635	C153	-1.0030224	1.4214296	-0.8194117	0.3649879
80	-0.4761	-2.5549	-0.8008	A60	C46	-1.0353834	-2.5511392	0.0634906	0.4757783
81	1.0102	-1.3455	0.9483	A186	C264	1.4868170	-1.5149655	0.8303546	0.2546760
82	-2.1061	1.9541	0.4877	A857	C76	-2.1614253	1.1751861	0.5762133	0.3075842
83	0.5324	-0.8526	0.1016	A325	C173	0.0988042	-1.1378972	-0.4550217	0.4251716
84	-1.2963	-0.0971	0.7140	A452	C127	-1.0331492	0.0055723	0.1700299	0.3032644
85	1.0031	0.3850	-0.3786	A483	C240	0.6514734	1.0103327	-0.5200428	0.3728007
86	-0.7562	0.7889	-0.4207	A580	C153	-1.0030224	1.4214296	-0.8194117	0.4260212
87	-0.4141	1.6829	-0.9637	A737	C153	-1.0030224	1.4214296	-0.8194117	0.3315604
88	-2.4210	-1.3252	-0.6499	A131	C67	-1.4757775	-1.2955060	-0.8486053	0.3912073
89	-1.6854	-0.3662	-0.9614	A425	C51	-2.2655670	0.0495469	-0.7279562	0.4097859
90	1.2558	-2.2969	-0.7863	A81	C193	0.8084450	-2.5111158	-0.3496015	0.3660898
91	-2.6405	-0.8162	-0.6455	A340	C51	-2.2655670	0.0495469	-0.7279562	0.4410454
92	0.8325	-0.9413	0.6689	A312	C264	1.4868170	-1.5149655	0.8303546	0.4631457
93	1.4609	-0.1864	0.8497	A431	C249	1.0778184	-0.1223857	0.3159433	0.3269509
94	-0.3355	0.9636	0.2005	A595	C197	-0.1968420	1.3899623	0.6958189	0.3534464
95	0.0714	1.3707	0.7787	A678	C197	-0.1968420	1.3899623	0.6958189	0.1234618
96	-1.0089	-0.6007	0.5639	A395	C127	-1.0331492	0.0055723	0.1700299	0.3414638
97	1.0072	-0.3094	-0.3233	A405	C249	1.0778184	-0.1223857	0.3159433	0.2989587
98	1.0167	0.2707	-0.3188	A483	C249	1.0778184	-0.1223857	0.3159433	0.3629824
99	0.5539	-0.8888	0.3037	A320	C249	1.0778184	-0.1223857	0.3159433	0.4341920
100	-0.0365	2.9667	0.2552	A889	C161	-1.0348261	2.5280129	0.2324966	0.4865722
101	1.3869	-2.0095	-0.8972	A86	C283	1.7808158	-0.9337703	-0.8105779	0.5187559
102	-0.6677	0.8863	-0.4552	A580	C153	-1.0030224	1.4214296	-0.8194117	0.4115546
103	0.8018	1.5204	0.9597	A728	C307	1.5763323	1.3461567	0.8384533	0.3566741
104	0.1104	1.7654	-0.9729	A781	C153	-1.0030224	1.4214296	-0.8194117	0.5369604
105	-1.7521	-1.6907	0.9005	A135	C35	-2.1242339	-0.9715258	0.7096658	0.4273808
106	-0.6146	1.0906	-0.6636	A635	C153	-1.0030224	1.4214296	-0.8194117	0.2916879
107	1.0107	0.3118	0.3349	A471	C249	1.0778184	-0.1223857	0.3159433	0.1734203
108	2.5043	0.9402	0.7378	A639	C307	1.5763323	1.3461567	0.8384533	0.4781926
109	2.2697	-0.3642	0.9543	A300	C340	2.6666782	-0.1317501	0.4147766	0.3896505
110	0.9096	0.4156	0.0115	A486	C249	1.0778184	-0.1223857	0.3159433	0.3368824
111	-0.5917	2.7188	-0.6227	A873	C161	-1.0348261	2.5280129	0.2324966	0.4963699
112	0.3515	0.9388	-0.0696	A585	C240	0.6514734	1.0103327	-0.5200428	0.2739830
113	0.0061	-1.0002	-0.0184	A302	C173	0.0988042	-1.1378972	-0.4550217	0.2223410
114	-1.0821	0.8067	-0.7597	A613	C153	-1.0030224	1.4214296	-0.8194117	0.2511729
115	2.8004	0.9339	-0.3059	A672	C330	2.2163811	0.9452850	-0.6878786	0.3257942
116	1.3163	1.9599	-0.9326	A783	C293	0.7212818	2.5491813	-0.2728450	0.6146848
117	-1.4733	-1.3145	0.9997	A221	C35	-2.1242339	-0.9715258	0.7096658	0.4279808
118	-0.2122	-2.6705	-0.7342	A60	C193	0.8084450	-2.5111158	-0.3496015	0.5215426
119	-2.6239	-0.2407	-0.7726	A446	C51	-2.2655670	0.0495469	-0.7279562	0.2310746
120	-1.0119	1.5636	-0.9905	A741	C153	-1.0030224	1.4214296	-0.8194117	0.1073788
121	-2.7687	0.9605	0.3660	A742	C76	-2.1614253	1.1751861	0.5762133	0.3440580
122	-1.5127	-0.2305	-0.8828	A449	C67	-1.4757775	-1.2955060	-0.8486053	0.3787077
123	-1.7557	-1.3185	-0.9807	A171	C67	-1.4757775	-1.2955060	-0.8486053	0.1450037
124	2.3165	1.2526	-0.7738	A709	C330	2.2163811	0.9452850	-0.6878786	0.1644518
125	-0.2336	0.9724	0.0084	A595	C197	-0.1968420	1.3899623	0.6958189	0.3805797
126	-0.5609	2.5334	-0.8039	A855	C161	-1.0348261	2.5280129	0.2324966	0.5052366
127	-0.5395	-0.8478	0.0993	A341	C127	-1.0331492	0.0055723	0.1700299	0.4725838
128	0.6976	2.5253	0.7847	A831	C293	0.7212818	2.5491813	-0.2728450	0.3683694
129	-2.0161	1.8310	-0.6904	A822	C153	-1.0030224	1.4214296	-0.8194117	0.5172199
130	-0.7381	0.6864	-0.1256	A550	C127	-1.0331492	0.0055723	0.1700299	0.4238356
131	-1.6351	0.6072	-0.9667	A555	C51	-2.2655670	0.0495469	-0.7279562	0.4756213
132	-1.3938	-1.5617	0.9956	A181	C144	-0.2145520	-1.5164273	0.7835631	0.4788525
133	-2.1713	-0.7846	0.9512	A366	C35	-2.1242339	-0.9715258	0.7096658	0.1585087
134	2.9855	-0.2779	-0.0572	A256	C340	2.6666782	-0.1317501	0.4147766	0.3123161
135	0.6609	0.7505	0.0094	A560	C240	0.6514734	1.0103327	-0.5200428	0.2662340
136	-2.0656	1.0148	0.9535	A712	C76	-2.1614253	1.1751861	0.5762133	0.2111660
137	2.0118	1.6641	0.7917	A760	C307	1.5763323	1.3461567	0.8384533	0.2667214
138	2.6854	0.0011	-0.7282	A420	C340	2.6666782	-0.1317501	0.4147766	0.4315162
139	0.2077	2.9580	0.2612	A889	C293	0.7212818	2.5491813	-0.2728450	0.4854818
140	1.1580	-0.0078	-0.5396	A429	C249	1.0778184	-0.1223857	0.3159433	0.3501035
141	2.4774	-0.1827	-0.8750	A380	C283	1.7808158	-0.9337703	-0.8105779	0.5040255
142	0.1572	2.8925	0.4426	A882	C293	0.7212818	2.5491813	-0.2728450	0.5409485
143	-1.6508	0.6997	-0.9783	A648	C51	-2.2655670	0.0495469	-0.7279562	0.5050880
144	-1.0394	1.0439	-0.8499	A650	C153	-1.0030224	1.4214296	-0.8194117	0.1481318
145	0.2042	-0.9885	-0.1366	A301	C173	0.0988042	-1.1378972	-0.4550217	0.1910716
146	1.6737	1.4277	0.9798	A714	C307	1.5763323	1.3461567	0.8384533	0.1067525
147	1.0109	2.2713	0.8739	A804	C307	1.5763323	1.3461567	0.8384533	0.5086741
148	-0.6493	1.4294	-0.9028	A689	C153	-1.0030224	1.4214296	-0.8194117	0.1483604
149	2.2479	-0.1014	0.9682	A407	C340	2.6666782	-0.1317501	0.4147766	0.3341839
150	-0.5288	1.7819	-0.9900	A737	C153	-1.0030224	1.4214296	-0.8194117	0.3350937
151	-0.7561	-0.6579	0.0675	A374	C127	-1.0331492	0.0055723	0.1700299	0.3476838
152	0.8472	0.6467	-0.3569	A523	C240	0.6514734	1.0103327	-0.5200428	0.2408340
153	0.0494	-1.5004	-0.8667	A191	C173	0.0988042	-1.1378972	-0.4550217	0.2745284
154	1.4575	-2.5965	-0.2104	A6	C193	0.8084450	-2.5111158	-0.3496015	0.2912135
155	-2.7065	1.2871	-0.0778	A828	C76	-2.1614253	1.1751861	0.5762133	0.4370006
156	-2.2093	-1.8571	0.4634	A94	C35	-2.1242339	-0.9715258	0.7096658	0.4056354
157	1.8719	-2.0979	0.5842	A53	C264	1.4868170	-1.5149655	0.8303546	0.4047240
158	-0.7712	1.7412	-0.9954	A757	C153	-1.0030224	1.4214296	-0.8194117	0.2425271
159	-1.8570	-0.4838	0.9967	A376	C35	-2.1242339	-0.9715258	0.7096658	0.3473313
160	-1.5575	-0.4091	-0.9210	A384	C67	-1.4757775	-1.2955060	-0.8486053	0.3468411
161	-0.4150	-2.4308	0.8848	A78	C144	-0.2145520	-1.5164273	0.7835631	0.4053525
162	-0.5571	1.0694	0.6077	A616	C197	-0.1968420	1.3899623	0.6958189	0.2563130
163	-2.7330	1.0858	0.3390	A818	C76	-2.1614253	1.1751861	0.5762133	0.2993914
164	1.0839	1.3601	0.9654	A694	C307	1.5763323	1.3461567	0.8384533	0.2111074
165	-1.0127	0.9834	-0.8086	A650	C153	-1.0030224	1.4214296	-0.8194117	0.1528396
166	0.6978	0.7200	0.0726	A549	C240	0.6514734	1.0103327	-0.5200428	0.3097673
167	1.5377	1.1223	-0.9954	A636	C330	2.2163811	0.9452850	-0.6878786	0.3877392
168	-2.7969	-0.8994	-0.3468	A209	C35	-2.1242339	-0.9715258	0.7096658	0.6004192
169	-2.8045	1.0304	0.1555	A778	C76	-2.1614253	1.1751861	0.5762133	0.4028580
170	1.1456	-0.0557	-0.5218	A429	C249	1.0778184	-0.1223857	0.3159433	0.3240702
171	-1.4904	1.4944	0.9939	A766	C76	-2.1614253	1.1751861	0.5762133	0.4693086
172	1.7280	-1.0702	0.9995	A212	C264	1.4868170	-1.5149655	0.8303546	0.2850313
173	-0.3749	-2.0941	0.9919	A112	C144	-0.2145520	-1.5164273	0.7835631	0.3154525
174	-0.1991	-2.8804	-0.4612	A32	C193	0.8084450	-2.5111158	-0.3496015	0.4961426
175	0.2616	1.8694	-0.9937	A748	C240	0.6514734	1.0103327	-0.5200428	0.5741993
176	2.9749	-0.3868	0.0046	A256	C340	2.6666782	-0.1317501	0.4147766	0.3244827
177	1.0074	1.1671	0.8888	A660	C307	1.5763323	1.3461567	0.8384533	0.2661119
178	0.0127	2.1162	-0.9932	A781	C293	0.7212818	2.5491813	-0.2728450	0.6206393
179	-0.9010	-0.6120	0.4128	A370	C127	-1.0331492	0.0055723	0.1700299	0.3308305
180	-2.2326	-2.0003	-0.0687	A70	C46	-1.0353834	-2.5511392	0.0634906	0.6267488
181	2.3736	-1.3232	0.6966	A116	C264	1.4868170	-1.5149655	0.8303546	0.4041010
182	-1.7240	-0.2263	0.9653	A427	C35	-2.1242339	-0.9715258	0.7096658	0.4670313
183	0.3635	1.2120	-0.6784	A643	C240	0.6514734	1.0103327	-0.5200428	0.2159993
184	0.0994	1.3382	0.7530	A678	C197	-0.1968420	1.3899623	0.6958189	0.1350618
185	0.9593	0.6731	-0.5605	A541	C240	0.6514734	1.0103327	-0.5200428	0.2285055
186	2.7482	-0.1387	-0.6595	A393	C340	2.6666782	-0.1317501	0.4147766	0.3875827
187	-0.7511	-2.2100	0.9425	A127	C144	-0.2145520	-1.5164273	0.7835631	0.4630192
188	0.8755	0.5009	-0.1315	A505	C240	0.6514734	1.0103327	-0.5200428	0.3740007
189	-0.2256	1.0650	-0.4116	A612	C240	0.6514734	1.0103327	-0.5200428	0.3467278
190	0.4280	-1.0208	-0.4498	A285	C173	0.0988042	-1.1378972	-0.4550217	0.1505049
191	1.8619	-1.8489	0.7815	A87	C264	1.4868170	-1.5149655	0.8303546	0.2526240
192	2.6100	-1.2196	0.4733	A116	C340	2.6666782	-0.1317501	0.4147766	0.4010172
193	-1.4064	0.6303	0.8885	A592	C76	-2.1614253	1.1751861	0.5762133	0.5373994
194	-2.8767	-0.7917	-0.1802	A209	C35	-2.1242339	-0.9715258	0.7096658	0.6073859
195	-2.3162	-0.8987	0.8748	A229	C35	-2.1242339	-0.9715258	0.7096658	0.1433087
196	-1.6482	1.1866	-0.9995	A697	C153	-1.0030224	1.4214296	-0.8194117	0.3533651
197	2.9111	-0.6332	0.2030	A205	C340	2.6666782	-0.1317501	0.4147766	0.3192161
198	-1.1111	-2.5855	-0.5806	A49	C46	-1.0353834	-2.5511392	0.0634906	0.2513893
199	1.0780	0.0770	0.3938	A448	C249	1.0778184	-0.1223857	0.3159433	0.0924747
200	-0.8611	0.5693	-0.2522	A551	C127	-1.0331492	0.0055723	0.1700299	0.3860023
201	-1.2703	0.5361	0.7836	A566	C127	-1.0331492	0.0055723	0.1700299	0.4604162
202	-1.1849	0.5412	0.7167	A566	C127	-1.0331492	0.0055723	0.1700299	0.4113495
203	1.1966	-1.0990	-0.9269	A249	C283	1.7808158	-0.9337703	-0.8105779	0.2885892
204	-1.5290	2.2697	0.6762	A856	C161	-1.0348261	2.5280129	0.2324966	0.3987301
205	-1.3309	2.3282	0.7316	A856	C161	-1.0348261	2.5280129	0.2324966	0.3316634
206	-0.1257	-1.0018	0.1387	A306	C173	0.0988042	-1.1378972	-0.4550217	0.3181077
207	-2.2637	-0.2444	0.9609	A443	C35	-2.1242339	-0.9715258	0.7096658	0.3726087
208	-0.5393	1.9492	-0.9997	A785	C153	-1.0030224	1.4214296	-0.8194117	0.3905937
209	-0.1142	1.0046	0.1482	A608	C197	-0.1968420	1.3899623	0.6958189	0.3385411
210	1.0132	0.3862	-0.4019	A483	C240	0.6514734	1.0103327	-0.5200428	0.3680007
211	0.5941	-0.8377	-0.2306	A328	C173	0.0988042	-1.1378972	-0.4550217	0.3399716
212	-1.6492	0.9503	0.9953	A700	C76	-2.1614253	1.1751861	0.5762133	0.3853994
213	1.9933	1.8745	0.6767	A802	C307	1.5763323	1.3461567	0.8384533	0.3690214
214	-2.2667	0.5608	-0.9422	A638	C51	-2.2655670	0.0495469	-0.7279562	0.2422100
215	0.5518	1.8579	0.9981	A753	C197	-0.1968420	1.3899623	0.6958189	0.5062870
216	-1.1263	-2.7706	0.1353	A35	C46	-1.0353834	-2.5511392	0.0634906	0.1273956
217	-2.6466	0.7281	-0.6671	A723	C51	-2.2655670	0.0495469	-0.7279562	0.3734808
218	1.2947	-0.5640	-0.8090	A359	C283	1.7808158	-0.9337703	-0.8105779	0.2858213
219	-0.4311	1.6988	-0.9689	A737	C153	-1.0030224	1.4214296	-0.8194117	0.3329271
220	-0.9296	-0.8628	-0.6816	A349	C67	-1.4757775	-1.2955060	-0.8486053	0.3819630
221	-0.4002	-1.4649	-0.8765	A194	C173	0.0988042	-1.1378972	-0.4550217	0.4158284
222	-0.7264	-0.6904	0.0655	A374	C127	-1.0331492	0.0055723	0.1700299	0.3690838
223	-0.0976	-0.9967	-0.0533	A302	C173	0.0988042	-1.1378972	-0.4550217	0.2464410
224	1.9171	1.7027	0.8257	A736	C307	1.5763323	1.3461567	0.8384533	0.2366881
225	0.2643	1.7851	0.9807	A764	C197	-0.1968420	1.3899623	0.6958189	0.3803870
226	0.4172	-1.2010	0.6849	A258	C144	-0.2145520	-1.5164273	0.7835631	0.3486141
227	-0.9629	-1.7392	0.9999	A170	C144	-0.2145520	-1.5164273	0.7835631	0.3958192
228	-0.9522	0.4025	-0.2578	A516	C127	-1.0331492	0.0055723	0.1700299	0.3019023
229	-1.2987	-1.0971	-0.9540	A234	C67	-1.4757775	-1.2955060	-0.8486053	0.1602927
230	1.8268	-2.1004	0.6211	A53	C264	1.4868170	-1.5149655	0.8303546	0.3782240
231	0.0457	2.7480	-0.6632	A864	C293	0.7212818	2.5491813	-0.2728450	0.4215852
232	-1.7364	2.4260	0.1816	A896	C161	-1.0348261	2.5280129	0.2324966	0.2848278
233	0.1392	-1.2656	0.6868	A241	C144	-0.2145520	-1.5164273	0.7835631	0.2337808
234	-1.0262	-0.0838	0.2416	A460	C127	-1.0331492	0.0055723	0.1700299	0.0559638
235	0.9986	-0.0710	-0.0482	A416	C249	1.0778184	-0.1223857	0.3159433	0.1649158
236	1.0814	-0.4312	0.5490	A360	C249	1.0778184	-0.1223857	0.3159433	0.1818176
237	1.7647	-0.7607	-0.9969	A317	C283	1.7808158	-0.9337703	-0.8105779	0.1251694
238	0.1266	-2.5965	-0.8003	A57	C193	0.8084450	-2.5111158	-0.3496015	0.4059759
239	-0.1443	1.2068	0.6200	A641	C197	-0.1968420	1.3899623	0.6958189	0.1038411
240	-1.0457	-0.0036	0.2987	A460	C127	-1.0331492	0.0055723	0.1700299	0.0501311
241	-0.8489	0.5665	0.2018	A544	C127	-1.0331492	0.0055723	0.1700299	0.2589823
242	-0.5389	-1.4186	0.8759	A207	C144	-0.2145520	-1.5164273	0.7835631	0.1715041
243	0.7198	-2.3073	-0.9089	A84	C193	0.8084450	-2.5111158	-0.3496015	0.2839198
244	1.9365	-2.0328	0.5898	A53	C264	1.4868170	-1.5149655	0.8303546	0.4026907
245	0.4322	-0.9950	0.4031	A297	C173	0.0988042	-1.1378972	-0.4550217	0.4448049
246	2.0087	-1.2122	-0.9382	A155	C283	1.7808158	-0.9337703	-0.8105779	0.2113120
247	2.8131	-0.4725	-0.5227	A242	C340	2.6666782	-0.1317501	0.4147766	0.4748827
248	-0.4136	-2.3388	-0.9270	A108	C46	-1.0353834	-2.5511392	0.0634906	0.6082044
249	1.9134	0.0457	-0.9963	A455	C283	1.7808158	-0.9337703	-0.8105779	0.4325922
250	1.8578	-1.4595	0.9320	A115	C264	1.4868170	-1.5149655	0.8303546	0.1760313
251	-0.7099	0.9201	-0.5458	A623	C153	-1.0030224	1.4214296	-0.8194117	0.3560212
252	2.1111	-0.9413	0.9502	A198	C264	1.4868170	-1.5149655	0.8303546	0.4392646
253	2.0386	-1.2636	-0.9172	A137	C283	1.7808158	-0.9337703	-0.8105779	0.2314120
254	-2.1045	-1.4548	0.8296	A165	C35	-2.1242339	-0.9715258	0.7096658	0.2076474
255	-1.2157	0.2006	-0.6406	A500	C127	-1.0331492	0.0055723	0.1700299	0.3960695
256	-1.0903	0.1837	-0.4475	A498	C127	-1.0331492	0.0055723	0.1700299	0.2842695
257	2.1908	-1.0273	0.9077	A198	C264	1.4868170	-1.5149655	0.8303546	0.4229980
258	-1.3952	-2.1031	-0.8518	A104	C67	-1.4757775	-1.2955060	-0.8486053	0.2971220
259	0.8937	1.2254	0.8755	A675	C307	1.5763323	1.3461567	0.8384533	0.2801453
260	2.7677	0.8184	-0.4634	A674	C330	2.2163811	0.9452850	-0.6878786	0.3008942
261	-1.5178	-2.0472	-0.8361	A104	C67	-1.4757775	-1.2955060	-0.8486053	0.2687406
262	0.2466	1.3024	0.7383	A663	C197	-0.1968420	1.3899623	0.6958189	0.1911618
263	-2.3220	-0.1687	-0.9446	A422	C51	-2.2655670	0.0495469	-0.7279562	0.1637746
264	-1.5469	2.1294	-0.7750	A836	C153	-1.0030224	1.4214296	-0.8194117	0.4320866
265	-0.9552	-1.0013	-0.7876	A275	C67	-1.4757775	-1.2955060	-0.8486053	0.2919296
266	0.1331	1.1610	-0.5557	A624	C240	0.6514734	1.0103327	-0.5200428	0.2348993
267	1.1512	-0.4325	-0.6378	A363	C283	1.7808158	-0.9337703	-0.8105779	0.4345546
268	-2.1630	1.9886	-0.3462	A876	C76	-2.1614253	1.1751861	0.5762133	0.5791340
269	0.2765	2.9550	0.2514	A889	C293	0.7212818	2.5491813	-0.2728450	0.4582818
270	0.9558	-0.3088	-0.0936	A391	C249	1.0778184	-0.1223857	0.3159433	0.2393253
271	0.7215	-0.7550	-0.2945	A328	C173	0.0988042	-1.1378972	-0.4550217	0.3887049
272	0.9587	1.8322	0.9977	A761	C307	1.5763323	1.3461567	0.8384533	0.4209741
273	-0.6577	2.1081	0.9781	A792	C197	-0.1968420	1.3899623	0.6958189	0.4870923
274	-1.1877	-0.6005	0.7432	A408	C127	-1.0331492	0.0055723	0.1700299	0.4445977
275	2.1446	1.2876	-0.8652	A698	C330	2.2163811	0.9452850	-0.6878786	0.1971392
276	-0.4185	-1.9997	-0.9991	A108	C67	-1.4757775	-1.2955060	-0.8486053	0.6373220
277	-0.5080	2.2976	0.9356	A815	C197	-0.1968420	1.3899623	0.6958189	0.4861923
278	-0.7465	2.4633	-0.8189	A855	C153	-1.0030224	1.4214296	-0.8194117	0.4329682
279	0.4541	-0.9390	0.2902	A303	C173	0.0988042	-1.1378972	-0.4550217	0.4331382
280	-2.2299	-1.8335	-0.4621	A96	C67	-1.4757775	-1.2955060	-0.8486053	0.5595406
281	0.7919	2.8503	-0.2860	A870	C293	0.7212818	2.5491813	-0.2728450	0.1282973
282	-0.6908	2.2020	-0.9514	A821	C153	-1.0030224	1.4214296	-0.8194117	0.4082604
283	-1.5171	2.2570	-0.6945	A836	C153	-1.0030224	1.4214296	-0.8194117	0.4915199
284	0.1077	0.9951	-0.0432	A593	C240	0.6514734	1.0103327	-0.5200428	0.3452830
285	-0.1726	-1.3383	-0.7594	A219	C173	0.0988042	-1.1378972	-0.4550217	0.2587284
286	-1.5178	2.1101	-0.8006	A836	C153	-1.0030224	1.4214296	-0.8194117	0.4074199
287	1.1208	-0.7868	-0.7761	A334	C283	1.7808158	-0.9337703	-0.8105779	0.2804880
288	0.9976	2.3613	-0.8262	A794	C293	0.7212818	2.5491813	-0.2728450	0.3391848
289	-0.0957	-2.2819	-0.9589	A90	C193	0.8084450	-2.5111158	-0.3496015	0.5808865
290	2.3610	0.6377	0.8952	A614	C307	1.5763323	1.3461567	0.8384533	0.5166237
291	-0.2239	-1.2077	0.6360	A260	C144	-0.2145520	-1.5164273	0.7835631	0.1552128
292	-2.7464	-0.4429	0.6234	A438	C35	-2.1242339	-0.9715258	0.7096658	0.4123526
293	-0.5055	1.6083	0.9494	A720	C197	-0.1968420	1.3899623	0.6958189	0.2601923
294	1.5636	-0.3040	0.9134	A381	C249	1.0778184	-0.1223857	0.3159433	0.4216176
295	-1.1940	-0.5640	0.7337	A408	C127	-1.0331492	0.0055723	0.1700299	0.4313644
296	0.3106	2.1351	-0.9875	A803	C293	0.7212818	2.5491813	-0.2728450	0.5131393
297	1.9919	-1.5481	0.8525	A114	C264	1.4868170	-1.5149655	0.8303546	0.1867876
298	0.7646	-0.9849	0.6578	A270	C264	1.4868170	-1.5149655	0.8303546	0.4749457
299	-0.9723	0.2434	-0.0681	A508	C127	-1.0331492	0.0055723	0.1700299	0.1789356
300	-0.4941	-1.1321	-0.6443	A261	C173	0.0988042	-1.1378972	-0.4550217	0.2626599
301	2.4906	0.7764	-0.7933	A633	C330	2.2163811	0.9452850	-0.6878786	0.1828417
302	1.6651	2.4151	0.3587	A861	C307	1.5763323	1.3461567	0.8384533	0.5458214
303	-0.6515	-0.9652	-0.5495	A298	C173	0.0988042	-1.1378972	-0.4550217	0.3391599
304	0.9636	-0.3203	0.1750	A409	C249	1.0778184	-0.1223857	0.3159433	0.1510253
305	-2.8681	-0.5478	-0.3921	A379	C51	-2.2655670	0.0495469	-0.7279562	0.5119120
306	0.1759	-1.2253	0.6474	A232	C144	-0.2145520	-1.5164273	0.7835631	0.2725808
307	0.9530	2.6293	-0.6044	A849	C293	0.7212818	2.5491813	-0.2728450	0.2144640
308	-1.3721	-2.6648	0.0734	A27	B1	-1.4461800	-2.6200500	-0.0738700	0.0887000
309	0.6497	0.7711	-0.1288	A540	C240	0.6514734	1.0103327	-0.5200428	0.2107496
310	1.8036	-0.2069	0.9828	A423	C249	1.0778184	-0.1223857	0.3159433	0.4923842
311	-1.3374	0.0159	-0.7490	A467	C51	-2.2655670	0.0495469	-0.7279562	0.3276192
312	-0.1616	-1.4889	0.8647	A199	C144	-0.2145520	-1.5164273	0.7835631	0.0538721
313	1.4913	0.8644	0.9611	A637	C307	1.5763323	1.3461567	0.8384533	0.2298119
314	-1.4797	1.9464	0.8956	A809	C161	-1.0348261	2.5280129	0.2324966	0.5631968
315	0.2746	1.2043	0.6443	A663	C197	-0.1968420	1.3899623	0.6958189	0.2362077
316	1.7734	-0.4621	-0.9859	A317	C283	1.7808158	-0.9337703	-0.8105779	0.2181361
317	2.9141	-0.0398	-0.4049	A393	C340	2.6666782	-0.1317501	0.4147766	0.3863495
318	0.5344	-0.9608	0.4346	A297	C249	1.0778184	-0.1223857	0.3159433	0.5001631
319	-1.8380	2.0072	-0.6923	A868	C153	-1.0030224	1.4214296	-0.8194117	0.5159532
320	0.9590	0.6964	0.5797	A524	C249	1.0778184	-0.1223857	0.3159433	0.4004536
321	-0.1324	-1.2128	0.6258	A260	C144	-0.2145520	-1.5164273	0.7835631	0.1811808
322	-1.0591	-0.6524	0.6544	A362	C127	-1.0331492	0.0055723	0.1700299	0.3894311
323	-1.9378	0.4456	-0.9999	A599	C51	-2.2655670	0.0495469	-0.7279562	0.3319213
324	-0.2104	-1.0150	-0.2679	A308	C173	0.0988042	-1.1378972	-0.4550217	0.2064077
325	-1.6349	-2.2681	-0.6054	A61	C67	-1.4757775	-1.2955060	-0.8486053	0.4583073
326	-0.9963	2.0788	0.9523	A807	C161	-1.0348261	2.5280129	0.2324966	0.4025141
327	-1.1840	0.7419	-0.7979	A613	C153	-1.0030224	1.4214296	-0.8194117	0.2940063
328	2.0068	1.8811	-0.6608	A770	C330	2.2163811	0.9452850	-0.6878786	0.3908249
329	0.3591	-1.1594	0.6179	A258	C144	-0.2145520	-1.5164273	0.7835631	0.3654475
330	1.9532	-1.9772	-0.6267	A67	C283	1.7808158	-0.9337703	-0.8105779	0.4665639
331	-1.2815	1.3119	0.9861	A730	C76	-2.1614253	1.1751861	0.5762133	0.4755086
332	-0.9525	-2.7196	-0.4721	A33	C46	-1.0353834	-2.5511392	0.0634906	0.2623116
333	-0.3423	-2.1263	0.9881	A112	C144	-0.2145520	-1.5164273	0.7835631	0.3140525
334	1.3654	-2.2420	0.7806	A75	C264	1.4868170	-1.5149655	0.8303546	0.2994020
335	1.9580	1.8141	0.7431	A802	C307	1.5763323	1.3461567	0.8384533	0.3149881
336	-2.4229	-1.2225	0.7003	A159	C35	-2.1242339	-0.9715258	0.7096658	0.1863354
337	-1.5901	0.5485	0.9481	A592	C76	-2.1614253	1.1751861	0.5762133	0.5232994
338	1.8350	2.1895	0.5156	A837	C307	1.5763323	1.3461567	0.8384533	0.4749547
339	0.6909	2.6899	-0.6292	A862	C293	0.7212818	2.5491813	-0.2728450	0.1758185
340	0.9264	-2.7371	-0.4567	A15	C193	0.8084450	-2.5111158	-0.3496015	0.1503459
341	-0.6307	1.7729	-0.9930	A757	C153	-1.0030224	1.4214296	-0.8194117	0.2991271
342	1.4671	2.1707	0.7846	A805	C307	1.5763323	1.3461567	0.8384533	0.3292096
343	-2.5332	-0.4550	0.8190	A383	C35	-2.1242339	-0.9715258	0.7096658	0.3449420
344	-0.1818	-1.1993	-0.6169	A246	C173	0.0988042	-1.1378972	-0.4550217	0.1679618
345	2.7015	-1.1361	0.3657	A130	C340	2.6666782	-0.1317501	0.4147766	0.3627494
346	0.3472	-1.7770	-0.9819	A136	C173	0.0988042	-1.1378972	-0.4550217	0.4714590
347	1.5341	1.2440	0.9997	A637	C307	1.5763323	1.3461567	0.8384533	0.1018786
348	0.9310	2.2616	-0.8952	A794	C293	0.7212818	2.5491813	-0.2728450	0.3732182
349	-2.0824	-0.4089	0.9925	A427	C35	-2.1242339	-0.9715258	0.7096658	0.2957646
350	-0.6190	-0.8094	0.1938	A358	C127	-1.0331492	0.0055723	0.1700299	0.4176305
351	0.5259	-2.3040	-0.9317	A84	C193	0.8084450	-2.5111158	-0.3496015	0.3572531
352	1.7592	-0.0228	-0.9706	A424	C283	1.7808158	-0.9337703	-0.8105779	0.3642027
353	1.9912	-2.0214	0.5465	A53	C264	1.4868170	-1.5149655	0.8303546	0.4315574
354	2.9498	0.5199	-0.0970	A548	C340	2.6666782	-0.1317501	0.4147766	0.4821828
355	1.3321	2.6876	0.0289	A877	C293	0.7212818	2.5491813	-0.2728450	0.3503273
356	-0.9611	0.5012	-0.4010	A517	C127	-1.0331492	0.0055723	0.1700299	0.3795689
357	-1.6531	2.2572	0.6029	A858	C161	-1.0348261	2.5280129	0.2324966	0.4198301
358	0.3262	2.4286	0.8928	A814	C293	0.7212818	2.5491813	-0.2728450	0.5604360
359	-1.4664	-1.0132	0.9760	A251	C35	-2.1242339	-0.9715258	0.7096658	0.3219474
360	-0.4140	-1.0491	0.4892	A289	C144	-0.2145520	-1.5164273	0.7835631	0.3203795
361	1.1056	0.7494	0.7474	A579	C307	1.5763323	1.3461567	0.8384533	0.3861808
362	-1.9118	2.1371	-0.4975	A868	C153	-1.0030224	1.4214296	-0.8194117	0.6487866
363	-0.4325	1.0009	0.4153	A622	C197	-0.1968420	1.3899623	0.6958189	0.3017464
364	1.8996	-1.1688	-0.9731	A155	C283	1.7808158	-0.9337703	-0.8105779	0.1721120
365	-1.5496	-2.5687	-0.0155	A27	B1	-1.4461800	-2.6200500	-0.0738700	0.0710467
366	-1.5943	-1.9291	0.8645	A105	C35	-2.1242339	-0.9715258	0.7096658	0.5474474
367	-1.9833	-1.8623	0.6934	A102	C35	-2.1242339	-0.9715258	0.7096658	0.3493247
368	-0.5589	-1.1118	0.6550	A277	C144	-0.2145520	-1.5164273	0.7835631	0.2925128
369	0.0034	2.6566	-0.7542	A851	C293	0.7212818	2.5491813	-0.2728450	0.4355518
370	2.4971	-1.2687	0.5987	A116	C264	1.4868170	-1.5149655	0.8303546	0.4960677
371	-0.5705	1.0938	0.6424	A616	C197	-0.1968420	1.3899623	0.6958189	0.2410797
372	0.5412	-2.7908	-0.5382	A30	C193	0.8084450	-2.5111158	-0.3496015	0.2451759
373	-0.9207	-2.1463	0.9421	A127	C46	-1.0353834	-2.5511392	0.0634906	0.4660440
374	0.7211	-0.8109	0.4038	A320	C249	1.0778184	-0.1223857	0.3159433	0.3776965
375	0.1512	-1.3657	0.7799	A232	C144	-0.2145520	-1.5164273	0.7835631	0.1733808
376	-2.4105	1.7635	-0.1623	A866	C76	-2.1614253	1.1751861	0.5762133	0.5253006
377	1.7594	-0.2690	0.9755	A345	C249	1.0778184	-0.1223857	0.3159433	0.4959176
378	1.2532	-2.4327	-0.6764	A37	C193	0.8084450	-2.5111158	-0.3496015	0.2833231
379	-2.7545	1.0746	-0.2910	A778	C76	-2.1614253	1.1751861	0.5762133	0.5202914
380	0.9407	2.0813	-0.9588	A794	C293	0.7212818	2.5491813	-0.2728450	0.4577515
381	1.6736	0.0349	0.9454	A423	C249	1.0778184	-0.1223857	0.3159433	0.4608413
382	1.5586	-2.1998	0.7181	A46	C264	1.4868170	-1.5149655	0.8303546	0.2896240
383	-2.6348	1.4243	0.0987	A828	C76	-2.1614253	1.1751861	0.5762133	0.4000006
384	-0.4232	2.9285	-0.2837	A891	C161	-1.0348261	2.5280129	0.2324966	0.5094366
385	-0.1376	-1.0364	0.2981	A293	C144	-0.2145520	-1.5164273	0.7835631	0.3474808
386	-1.0417	-0.6541	0.6381	A362	C127	-1.0331492	0.0055723	0.1700299	0.3787644
387	-1.9399	-2.2145	-0.3298	A48	C46	-1.0353834	-2.5511392	0.0634906	0.5448155
388	0.9920	1.4959	-0.9787	A707	C240	0.6514734	1.0103327	-0.5200428	0.4282504
389	0.9481	-1.5105	0.9763	A186	C264	1.4868170	-1.5149655	0.8303546	0.2297093
390	1.0106	-2.4281	0.7766	A52	C193	0.8084450	-2.5111158	-0.3496015	0.4704574
391	-2.8402	-0.5754	-0.4402	A379	C51	-2.2655670	0.0495469	-0.7279562	0.4957787
392	-0.2000	-2.5435	0.8343	A73	C144	-0.2145520	-1.5164273	0.7835631	0.3641205
393	1.5181	-0.5919	-0.9288	A348	C283	1.7808158	-0.9337703	-0.8105779	0.2409361
394	2.6253	-1.1065	0.5285	A130	C340	2.6666782	-0.1317501	0.4147766	0.3766172
395	-1.4272	-0.0873	0.8216	A464	C127	-1.0331492	0.0055723	0.1700299	0.3794977
396	-2.0542	-0.3475	0.9965	A427	C35	-2.1242339	-0.9715258	0.7096658	0.3269646
397	-0.1654	1.3321	0.7533	A682	C197	-0.1968420	1.3899623	0.6958189	0.0489285
398	-1.1408	-0.3887	-0.6068	A419	C127	-1.0331492	0.0055723	0.1700299	0.4262510
399	-0.9040	0.4336	-0.0729	A516	C127	-1.0331492	0.0055723	0.1700299	0.2667023
400	-0.8225	2.6513	-0.6308	A855	C161	-1.0348261	2.5280129	0.2324966	0.3996366
401	-0.9434	2.6676	0.5584	A883	C161	-1.0348261	2.5280129	0.2324966	0.1856389
402	1.6575	1.1324	-1.0000	A636	C330	2.2163811	0.9452850	-0.6878786	0.3527058
403	0.9318	0.3663	0.0501	A486	C249	1.0778184	-0.1223857	0.3159433	0.3001824
404	1.6784	0.2716	-0.9540	A477	C283	1.7808158	-0.9337703	-0.8105779	0.4837361
405	-1.3191	0.0306	0.7327	A475	C127	-1.0331492	0.0055723	0.1700299	0.2912162
406	-0.7213	-2.2127	0.9449	A127	C144	-0.2145520	-1.5164273	0.7835631	0.4547859
407	-0.8939	-0.4483	0.0070	A399	C127	-1.0331492	0.0055723	0.1700299	0.2520505
408	1.0038	-0.3270	0.3290	A392	C249	1.0778184	-0.1223857	0.3159433	0.0972298
409	-0.4093	-2.1522	0.9816	A112	C144	-0.2145520	-1.5164273	0.7835631	0.3428525
410	-0.1436	1.7244	0.9630	A747	C197	-0.1968420	1.3899623	0.6958189	0.2182870
411	1.1471	0.6702	0.7410	A524	C307	1.5763323	1.3461567	0.8384533	0.4008808
412	2.8078	-0.9541	0.2606	A158	C340	2.6666782	-0.1317501	0.4147766	0.3725494
413	-0.6396	-2.6804	0.6549	A64	C46	-1.0353834	-2.5511392	0.0634906	0.3721512
414	-1.7234	0.1759	-0.9635	A491	C51	-2.2655670	0.0495469	-0.7279562	0.3013546
415	-2.1670	-2.0723	0.0569	A70	C46	-1.0353834	-2.5511392	0.0634906	0.5390155
416	-1.8182	-0.0682	-0.9836	A425	C51	-2.2655670	0.0495469	-0.7279562	0.2735859
417	-1.2888	0.2845	-0.7331	A496	C51	-2.2655670	0.0495469	-0.7279562	0.4056213
418	-1.4372	2.3147	-0.6892	A879	C153	-1.0030224	1.4214296	-0.8194117	0.4858866
419	-2.0814	2.1240	0.2275	A884	C76	-2.1614253	1.1751861	0.5762133	0.4591842
420	-1.0933	0.7698	-0.7487	A613	C153	-1.0030224	1.4214296	-0.8194117	0.2708729
421	2.0184	2.0456	-0.4864	A833	C330	2.2163811	0.9452850	-0.6878786	0.4999249
422	-0.6250	-2.3935	-0.8807	A71	C46	-1.0353834	-2.5511392	0.0634906	0.5040711
423	-0.7592	0.6589	0.1023	A567	C127	-1.0331492	0.0055723	0.1700299	0.3316689
424	-0.4106	1.2874	-0.7610	A680	C153	-1.0030224	1.4214296	-0.8194117	0.2616212
425	-2.8204	0.5687	-0.4803	A711	C51	-2.2655670	0.0495469	-0.7279562	0.4405474
426	-0.5527	0.8375	-0.0827	A581	C127	-1.0331492	0.0055723	0.1700299	0.5217023
427	0.3583	1.3247	-0.7784	A643	C240	0.6514734	1.0103327	-0.5200428	0.2886327
428	1.4578	-1.9239	0.9104	A103	C264	1.4868170	-1.5149655	0.8303546	0.1726657
429	-0.3630	-2.3799	0.9132	A78	C144	-0.2145520	-1.5164273	0.7835631	0.3805192
430	-1.3088	2.5076	-0.5598	A879	C161	-1.0348261	2.5280129	0.2324966	0.3622278
431	-1.2775	-0.1572	-0.7013	A444	C51	-2.2655670	0.0495469	-0.7279562	0.4071567
432	1.7320	-0.8994	-0.9988	A187	C283	1.7808158	-0.9337703	-0.8105779	0.0904694
433	1.9608	0.3359	0.9999	A470	C307	1.5763323	1.3461567	0.8384533	0.5187237
434	0.5631	-1.1426	0.6875	A264	C144	-0.2145520	-1.5164273	0.7835631	0.4158475
435	-0.6149	0.7934	-0.0864	A570	C127	-1.0331492	0.0055723	0.1700299	0.4875023
436	-1.4499	2.5021	0.4523	A888	C161	-1.0348261	2.5280129	0.2324966	0.2202634
437	-1.9820	-1.0679	-0.9679	A190	C67	-1.4757775	-1.2955060	-0.8486053	0.2843744
438	2.3895	0.3600	-0.9091	A478	C330	2.2163811	0.9452850	-0.6878786	0.3265417
439	-2.7236	0.7725	-0.5562	A763	C51	-2.2655670	0.0495469	-0.7279562	0.4509141
440	1.2417	0.2147	0.6728	A494	C249	1.0778184	-0.1223857	0.3159433	0.2859413
441	-2.6521	-1.0815	-0.5032	A184	C67	-1.4757775	-1.2955060	-0.8486053	0.5785780
442	-1.3743	1.2884	0.9932	A730	C76	-2.1614253	1.1751861	0.5762133	0.4391086
443	-2.1078	0.5587	0.9836	A604	C76	-2.1614253	1.1751861	0.5762133	0.3591660
444	1.2801	-1.1524	0.9607	A210	C264	1.4868170	-1.5149655	0.8303546	0.2332093
445	-1.3070	-0.3265	-0.7575	A418	C67	-1.4757775	-1.2955060	-0.8486053	0.4096296
446	-0.0306	-2.7661	0.6425	A43	C144	-0.2145520	-1.5164273	0.7835631	0.5248959
447	-1.0606	1.6690	-0.9997	A741	C153	-1.0030224	1.4214296	-0.8194117	0.1618121
448	-1.0179	0.2927	0.3389	A509	C127	-1.0331492	0.0055723	0.1700299	0.1570823
449	0.9382	-1.8460	0.9975	A144	C264	1.4868170	-1.5149655	0.8303546	0.3489323
450	2.9133	0.1497	-0.3986	A442	C340	2.6666782	-0.1317501	0.4147766	0.4471495
451	0.4691	0.9176	-0.2451	A576	C240	0.6514734	1.0103327	-0.5200428	0.1833496
452	0.9005	2.3979	0.8275	A831	C293	0.7212818	2.5491813	-0.2728450	0.4769482
453	1.6013	-0.3146	0.9298	A381	C249	1.0778184	-0.1223857	0.3159433	0.4431842
454	1.9487	-1.1794	0.9606	A161	C264	1.4868170	-1.5149655	0.8303546	0.3092313
455	-2.4310	-1.7577	-0.0142	A109	C35	-2.1242339	-0.9715258	0.7096658	0.6056020
456	-0.1516	-1.8257	-0.9858	A150	C173	0.0988042	-1.1378972	-0.4550217	0.4896618
457	-1.7181	-1.9321	0.8107	A105	C35	-2.1242339	-0.9715258	0.7096658	0.4892474
458	1.4558	2.4311	-0.5523	A846	C293	0.7212818	2.5491813	-0.2728450	0.3773515
459	-1.8161	2.2416	-0.4657	A893	C161	-1.0348261	2.5280129	0.2324966	0.5886278
460	-2.7993	-0.0222	0.6008	A476	C35	-2.1242339	-0.9715258	0.7096658	0.5777526
461	-2.2591	1.8710	-0.3590	A876	C76	-2.1614253	1.1751861	0.5762133	0.5762340
462	-0.2441	2.3910	-0.9150	A832	C293	0.7212818	2.5491813	-0.2728450	0.5885727
463	-1.7852	-1.0705	-0.9967	A214	C67	-1.4757775	-1.2955060	-0.8486053	0.2275077
464	0.3546	-1.0268	0.4065	A283	C173	0.0988042	-1.1378972	-0.4550217	0.4094716
465	2.4420	-1.1741	-0.7046	A147	C283	1.7808158	-0.9337703	-0.8105779	0.3358306
466	-0.1455	-1.0169	0.2321	A293	C173	0.0988042	-1.1378972	-0.4550217	0.3508077
467	-1.2586	-0.6983	0.8280	A350	C35	-2.1242339	-0.9715258	0.7096658	0.4190646
468	-0.6749	2.4205	0.8585	A835	C161	-1.0348261	2.5280129	0.2324966	0.3644808
469	1.8836	-1.6761	-0.8534	A106	C283	1.7808158	-0.9337703	-0.8105779	0.2959787
470	0.9794	0.2564	-0.1571	A484	C249	1.0778184	-0.1223857	0.3159433	0.3167491
471	0.1168	-1.2793	-0.6987	A219	C173	0.0988042	-1.1378972	-0.4550217	0.1343590
472	0.9442	0.6967	-0.5629	A541	C240	0.6514734	1.0103327	-0.5200428	0.2164055
473	2.3139	-1.3026	-0.7553	A137	C283	1.7808158	-0.9337703	-0.8105779	0.3190639
474	-0.8976	-1.5233	0.9727	A196	C144	-0.2145520	-1.5164273	0.7835631	0.2930192
475	0.4539	-2.9638	-0.0575	A5	C193	0.8084450	-2.5111158	-0.3496015	0.3664436
476	-2.6448	-0.7762	0.6542	A282	C35	-2.1242339	-0.9715258	0.7096658	0.2571192
477	-1.5878	2.3892	-0.4954	A879	C161	-1.0348261	2.5280129	0.2324966	0.4732278
478	1.3027	-2.5447	-0.5124	A37	C193	0.8084450	-2.5111158	-0.3496015	0.2302125
479	-2.9767	-0.3382	-0.0907	A400	C51	-2.2655670	0.0495469	-0.7279562	0.5787120
480	-1.8080	-0.5939	-0.9953	A385	C67	-1.4757775	-1.2955060	-0.8486053	0.3935077
481	0.6148	-0.8022	-0.1460	A328	C173	0.0988042	-1.1378972	-0.4550217	0.3869049
482	1.1166	0.4132	0.5873	A488	C249	1.0778184	-0.1223857	0.3159433	0.2819080
483	1.0180	0.0346	-0.1917	A447	C249	1.0778184	-0.1223857	0.3159433	0.2414824
484	1.9473	0.4710	-1.0000	A499	C330	2.2163811	0.9452850	-0.6878786	0.3518291
485	-1.0920	-2.1752	-0.9009	A77	C67	-1.4757775	-1.2955060	-0.8486053	0.4385887
486	1.2253	-2.3688	-0.7451	A37	C193	0.8084450	-2.5111158	-0.3496015	0.3182231
487	0.0969	2.9984	0.0054	A889	C293	0.7212818	2.5491813	-0.2728450	0.4506152
488	1.5214	-0.5161	0.9194	A347	C264	1.4868170	-1.5149655	0.8303546	0.3741646
489	-1.1951	1.9945	-0.9457	A816	C153	-1.0030224	1.4214296	-0.8194117	0.2971454
490	-1.8806	-0.9671	0.9934	A267	C35	-2.1242339	-0.9715258	0.7096658	0.1772646
491	2.9041	-0.7280	0.1098	A158	C340	2.6666782	-0.1317501	0.4147766	0.3795494
492	-2.4917	-1.0483	-0.7110	A184	C51	-2.2655670	0.0495469	-0.7279562	0.4469787
493	2.0934	-1.5943	-0.7755	A106	C283	1.7808158	-0.9337703	-0.8105779	0.3360639
494	-2.8118	-0.5004	0.5171	A414	C35	-2.1242339	-0.9715258	0.7096658	0.4504192
495	2.0338	0.9379	-0.9708	A625	C330	2.2163811	0.9452850	-0.6878786	0.1576291
496	1.4359	-1.0224	0.9714	A236	C264	1.4868170	-1.5149655	0.8303546	0.2281760
497	-1.4013	-2.6400	-0.1488	A27	B1	-1.4461800	-2.6200500	-0.0738700	0.0465867
498	1.4745	2.2820	0.6971	A805	C307	1.5763323	1.3461567	0.8384533	0.3930096
499	-2.9766	-0.3728	-0.0168	A400	C51	-2.2655670	0.0495469	-0.7279562	0.6148454
500	2.5135	-1.2599	0.5843	A116	C340	2.6666782	-0.1317501	0.4147766	0.4836172
501	-0.1332	-2.9322	0.3540	A18	C46	-1.0353834	-2.5511392	0.0634906	0.5245845
502	2.8533	0.2470	0.5036	A469	C340	2.6666782	-0.1317501	0.4147766	0.2180651
503	2.9432	0.2305	-0.3053	A466	C340	2.6666782	-0.1317501	0.4147766	0.4529495
504	1.6653	1.0301	0.9991	A637	C307	1.5763323	1.3461567	0.8384533	0.1885570
505	1.2618	-0.5789	-0.7911	A359	C283	1.7808158	-0.9337703	-0.8105779	0.2977880
506	-2.0793	1.1458	-0.9274	A733	C153	-1.0030224	1.4214296	-0.8194117	0.4866318
507	-0.2092	-0.9897	0.1514	A306	C173	0.0988042	-1.1378972	-0.4550217	0.3542077
508	2.6611	-0.7924	-0.6300	A172	C283	1.7808158	-0.9337703	-0.8105779	0.4007441
509	0.5795	-2.8524	0.4132	A24	C193	0.8084450	-2.5111158	-0.3496015	0.4443436
510	2.3855	-1.5136	0.5649	A98	C264	1.4868170	-1.5149655	0.8303546	0.3885010
511	-0.5500	0.9269	-0.3868	A598	C153	-1.0030224	1.4214296	-0.8194117	0.4600546
512	2.7959	0.3429	0.5769	A469	C340	2.6666782	-0.1317501	0.4147766	0.2553318
513	1.1593	1.1597	0.9329	A660	C307	1.5763323	1.3461567	0.8384533	0.2326453
514	-1.0709	-1.0845	-0.8795	A268	C67	-1.4757775	-1.2955060	-0.8486053	0.2155927
515	0.7434	-2.8441	0.3421	A13	C193	0.8084450	-2.5111158	-0.3496015	0.3632436
516	1.6102	-1.3687	0.9936	A177	C264	1.4868170	-1.5149655	0.8303546	0.1442980
517	-0.4159	-0.9144	0.0949	A329	C173	0.0988042	-1.1378972	-0.4550217	0.4293744
518	-1.3758	0.4363	0.8307	A531	C127	-1.0331492	0.0055723	0.1700299	0.4780162
519	-0.8939	2.8442	0.1923	A898	C161	-1.0348261	2.5280129	0.2324966	0.1657699
520	-2.2664	-1.5110	-0.6898	A131	C67	-1.4757775	-1.2955060	-0.8486053	0.3883073
521	-0.1395	-1.6332	-0.9326	A150	C173	0.0988042	-1.1378972	-0.4550217	0.4037284
522	0.5661	0.8244	-0.0101	A560	C240	0.6514734	1.0103327	-0.5200428	0.2604163
523	2.5715	1.3977	0.3755	A725	C307	1.5763323	1.3461567	0.8384533	0.5032214
524	1.0013	0.3344	0.3290	A471	C249	1.0778184	-0.1223857	0.3159433	0.1821203
525	2.7018	1.1923	0.3025	A725	C340	2.6666782	-0.1317501	0.4147766	0.4904828
526	1.4018	2.6324	0.1869	A871	C293	0.7212818	2.5491813	-0.2728450	0.4078273
527	-1.1754	2.5608	-0.5757	A880	C161	-1.0348261	2.5280129	0.2324966	0.3271859
528	2.0208	-2.2094	0.1075	A23	B2	1.9932630	-2.2208778	0.0463593	0.0333852
529	1.4881	1.4011	-0.9990	A666	C330	2.2163811	0.9452850	-0.6878786	0.4984058
530	0.2971	-2.5814	-0.8011	A54	C193	0.8084450	-2.5111158	-0.3496015	0.3443759
531	-0.1033	1.0084	-0.1649	A603	C240	0.6514734	1.0103327	-0.5200428	0.3706163
532	1.0450	-0.8073	0.7337	A319	C249	1.0778184	-0.1223857	0.3159433	0.3784965
533	1.0334	0.1543	-0.2962	A441	C249	1.0778184	-0.1223857	0.3159433	0.3110824
534	-2.9704	0.2639	0.1884	A620	C51	-2.2655670	0.0495469	-0.7279562	0.6118474
535	0.8168	-2.7717	-0.4569	A15	C193	0.8084450	-2.5111158	-0.3496015	0.1254125
536	-2.2817	-0.4067	-0.9482	A371	C51	-2.2655670	0.0495469	-0.7279562	0.2308746
537	1.6355	0.9841	0.9958	A637	C307	1.5763323	1.3461567	0.8384533	0.1928570
538	-1.7208	2.0582	0.7306	A858	C76	-2.1614253	1.1751861	0.5762133	0.4926753
539	-1.4891	1.3461	-1.0000	A706	C153	-1.0030224	1.4214296	-0.8194117	0.2473318
540	-1.2745	2.3258	-0.7581	A816	C153	-1.0030224	1.4214296	-0.8194117	0.4123866
541	-0.3747	0.9601	0.2456	A597	C197	-0.1968420	1.3899623	0.6958189	0.3526464
542	-0.6509	-0.7717	-0.1378	A343	C173	0.0988042	-1.1378972	-0.4550217	0.4777077
543	-2.1910	1.4019	0.7992	A775	C76	-2.1614253	1.1751861	0.5762133	0.1597584
544	-2.3114	-0.8650	-0.8838	A230	C51	-2.2655670	0.0495469	-0.7279562	0.3720746
545	1.9179	1.3814	0.9315	A702	C307	1.5763323	1.3461567	0.8384533	0.1566192
546	2.8612	0.3393	0.4726	A495	C340	2.6666782	-0.1317501	0.4147766	0.2411318
547	-0.4060	-1.8194	0.9907	A141	C144	-0.2145520	-1.5164273	0.7835631	0.2338525
548	-0.9695	-1.4361	0.9636	A223	C144	-0.2145520	-1.5164273	0.7835631	0.3384374
549	-2.3125	-0.5263	-0.9284	A371	C51	-2.2655670	0.0495469	-0.7279562	0.2744079
550	0.7288	0.7442	0.2855	A549	C240	0.6514734	1.0103327	-0.5200428	0.3830007
551	2.2831	0.0150	-0.9591	A401	C330	2.2163811	0.9452850	-0.6878786	0.4227417
552	-2.5635	1.5580	-0.0168	A866	C76	-2.1614253	1.1751861	0.5762133	0.4593006
553	0.9634	0.2999	0.1341	A487	C249	1.0778184	-0.1223857	0.3159433	0.2395158
554	0.9435	-0.4398	-0.2834	A405	C249	1.0778184	-0.1223857	0.3159433	0.3503587
555	1.7940	-2.3567	0.2737	A11	C264	1.4868170	-1.5149655	0.8303546	0.5685240
556	-1.8007	0.5261	-0.9923	A599	C51	-2.2655670	0.0495469	-0.7279562	0.4019213
557	0.9055	0.5011	-0.2618	A501	C240	0.6514734	1.0103327	-0.5200428	0.3405007
558	0.0628	2.5775	0.8159	A852	C197	-0.1968420	1.3899623	0.6958189	0.5224203
559	1.3519	-2.3223	-0.7265	A37	C193	0.8084450	-2.5111158	-0.3496015	0.3697231
560	-1.0849	2.5629	0.6219	A859	C161	-1.0348261	2.5280129	0.2324966	0.1581215
561	2.1467	-0.6454	0.9704	A300	C340	2.6666782	-0.1317501	0.4147766	0.5297505
562	-0.1052	1.0548	-0.3414	A606	C240	0.6514734	1.0103327	-0.5200428	0.3265945
563	1.6380	1.3371	0.9934	A679	C307	1.5763323	1.3461567	0.8384533	0.0752237
564	1.7682	0.6180	-0.9919	A511	C330	2.2163811	0.9452850	-0.6878786	0.3598291
565	-1.2428	-2.7287	0.0575	A34	C46	-1.0353834	-2.5511392	0.0634906	0.1303227
566	-0.0286	1.0078	0.1275	A601	C197	-0.1968420	1.3899623	0.6958189	0.3729077
567	0.8838	-1.0687	0.7899	A270	C264	1.4868170	-1.5149655	0.8303546	0.3632457
568	2.8096	-0.4410	0.5364	A244	C340	2.6666782	-0.1317501	0.4147766	0.1912650
569	-1.9040	1.6712	-0.8459	A822	C153	-1.0030224	1.4214296	-0.8194117	0.3924121
570	-2.1066	-1.5975	-0.7652	A134	C67	-1.4757775	-1.2955060	-0.8486053	0.3387406
571	0.3431	-1.4005	-0.8298	A222	C173	0.0988042	-1.1378972	-0.4550217	0.2938923
572	-0.9596	1.1975	-0.8851	A676	C153	-1.0030224	1.4214296	-0.8194117	0.1110134
573	-2.0167	-0.5151	-0.9967	A385	C51	-2.2655670	0.0495469	-0.7279562	0.3607526
574	-0.5430	2.9036	-0.3000	A891	C161	-1.0348261	2.5280129	0.2324966	0.4666366
575	-2.2482	-0.0852	0.9683	A443	C35	-2.1242339	-0.9715258	0.7096658	0.4229753
576	-0.7845	0.6248	0.0766	A550	C127	-1.0331492	0.0055723	0.1700299	0.3204356
577	0.2263	2.9654	-0.2266	A885	C293	0.7212818	2.5491813	-0.2728450	0.3191485
578	-0.1932	-1.2543	-0.6824	A246	C173	0.0988042	-1.1378972	-0.4550217	0.2119284
579	0.8000	-0.9510	-0.6531	A271	C173	0.0988042	-1.1378972	-0.4550217	0.3620571
580	1.4962	-0.2775	-0.8782	A397	C283	1.7808158	-0.9337703	-0.8105779	0.3361694
581	-2.6190	0.9850	-0.6025	A763	C51	-2.2655670	0.0495469	-0.7279562	0.4714474
582	1.2370	2.0652	-0.9133	A783	C293	0.7212818	2.5491813	-0.2728450	0.5467182
583	-2.0875	-0.8865	0.9634	A267	C35	-2.1242339	-0.9715258	0.7096658	0.1251646
584	2.2794	-0.9395	-0.8851	A185	C283	1.7808158	-0.9337703	-0.8105779	0.1929454
585	-1.8841	2.0159	0.6508	A857	C76	-2.1614253	1.1751861	0.5762133	0.3975420
586	-0.5941	1.3851	-0.8701	A689	C153	-1.0030224	1.4214296	-0.8194117	0.1653134
587	2.4038	-0.8914	0.8260	A201	C340	2.6666782	-0.1317501	0.4147766	0.4779172
588	2.8843	0.0332	-0.4666	A393	C340	2.6666782	-0.1317501	0.4147766	0.4213162
589	1.7385	-2.4288	-0.1615	A2	B2	1.9932630	-2.2208778	0.0463593	0.2235148
590	0.9927	-0.2388	0.2041	A409	C249	1.0778184	-0.1223857	0.3159433	0.1044587
591	2.1378	-0.2369	-0.9885	A401	C283	1.7808158	-0.9337703	-0.8105779	0.4105922
592	-1.3518	0.9633	0.9404	A649	C76	-2.1614253	1.1751861	0.5762133	0.4618994
593	-1.2023	0.2876	-0.6455	A500	C127	-1.0331492	0.0055723	0.1700299	0.4222362
594	-0.7710	-1.7342	-0.9948	A157	C67	-1.4757775	-1.2955060	-0.8486053	0.4298887
595	-1.2257	-1.7894	-0.9856	A138	C67	-1.4757775	-1.2955060	-0.8486053	0.2936554
596	-1.0372	2.7567	-0.3259	A894	C161	-1.0348261	2.5280129	0.2324966	0.2631525
597	-2.7297	-0.8602	0.5069	A282	C35	-2.1242339	-0.9715258	0.7096658	0.3065192
598	-1.2891	2.1033	0.8843	A810	C161	-1.0348261	2.5280129	0.2324966	0.4435968
599	-0.0794	-1.3343	-0.7483	A219	C173	0.0988042	-1.1378972	-0.4550217	0.2226284
600	-1.6496	1.3014	0.9949	A740	C76	-2.1614253	1.1751861	0.5762133	0.3522420
601	0.6172	-0.8195	0.2263	A325	C249	1.0778184	-0.1223857	0.3159433	0.4157920
602	-0.0008	-1.2084	-0.6110	A248	C173	0.0988042	-1.1378972	-0.4550217	0.1086951
603	-1.1207	0.7282	0.7481	A588	C127	-1.0331492	0.0055723	0.1700299	0.4627495
604	1.5386	1.5472	-0.9833	A724	C330	2.2163811	0.9452850	-0.6878786	0.5250392
605	2.5591	1.5461	-0.1419	A767	C330	2.2163811	0.9452850	-0.6878786	0.4965042
606	-1.0278	0.2923	0.3639	A509	C127	-1.0331492	0.0055723	0.1700299	0.1619823
607	-1.5219	-0.5056	-0.9181	A384	C67	-1.4757775	-1.2955060	-0.8486053	0.3018411
608	-2.7733	1.1066	-0.1675	A778	C76	-2.1614253	1.1751861	0.5762133	0.4747247
609	0.5690	0.9242	-0.4042	A589	C240	0.6514734	1.0103327	-0.5200428	0.0948163
610	-1.1517	-1.3108	-0.9669	A234	C67	-1.4757775	-1.2955060	-0.8486053	0.1525554
611	0.4789	1.6690	-0.9646	A699	C240	0.6514734	1.0103327	-0.5200428	0.4252660
612	0.9753	-0.5500	-0.4744	A361	C249	1.0778184	-0.1223857	0.3159433	0.4401587
613	2.0866	-2.1150	0.2388	A23	B2	1.9932630	-2.2208778	0.0463593	0.1305519
614	-0.9672	-0.2558	-0.0286	A432	C127	-1.0331492	0.0055723	0.1700299	0.1753171
615	1.1526	0.0293	0.5316	A457	C249	1.0778184	-0.1223857	0.3159433	0.1473747
616	1.0557	-0.9141	0.7973	A272	C264	1.4868170	-1.5149655	0.8303546	0.3550124
617	-2.9825	0.3033	0.0646	A669	C51	-2.2655670	0.0495469	-0.7279562	0.5877474
618	-1.8615	-1.1457	-0.9826	A214	C67	-1.4757775	-1.2955060	-0.8486053	0.2231744
619	-1.1406	0.3513	0.5913	A527	C127	-1.0331492	0.0055723	0.1700299	0.2914829
620	1.9821	-2.2520	0.0038	A2	B2	1.9932630	-2.2208778	0.0463593	0.0282815
621	1.3409	0.7729	0.8919	A543	C307	1.5763323	1.3461567	0.8384533	0.2873786
622	-1.1470	0.0351	0.5227	A463	C127	-1.0331492	0.0055723	0.1700299	0.1653495
623	-2.4216	0.1088	-0.9056	A537	C51	-2.2655670	0.0495469	-0.7279562	0.1309766
624	1.3844	0.2719	0.8081	A490	C249	1.0778184	-0.1223857	0.3159433	0.3976747
625	-0.9681	-0.6976	0.5909	A362	C127	-1.0331492	0.0055723	0.1700299	0.3963638
626	-2.1058	2.0946	0.2426	A884	C76	-2.1614253	1.1751861	0.5762133	0.4362175
627	-1.2226	0.2830	-0.6670	A500	C127	-1.0331492	0.0055723	0.1700299	0.4346362
628	1.5198	2.0861	0.8139	A805	C307	1.5763323	1.3461567	0.8384533	0.2736763
629	0.4118	1.2926	-0.7656	A643	C240	0.6514734	1.0103327	-0.5200428	0.2558327
630	-1.1705	0.8918	-0.8489	A613	C153	-1.0030224	1.4214296	-0.8194117	0.2421985
631	1.9110	-0.7038	0.9993	A239	C264	1.4868170	-1.5149655	0.8303546	0.4680980
632	0.2552	1.0964	0.4854	A619	C197	-0.1968420	1.3899623	0.6958189	0.3186744
633	-2.9023	-0.0823	-0.4287	A529	C51	-2.2655670	0.0495469	-0.7279562	0.3559454
634	-1.3259	-0.6196	0.8439	A396	C35	-2.1242339	-0.9715258	0.7096658	0.4281646
635	-0.5238	1.7526	-0.9853	A737	C153	-1.0030224	1.4214296	-0.8194117	0.3254271
636	1.2776	-1.1577	-0.9612	A206	C283	1.7808158	-0.9337703	-0.8105779	0.2925892
637	1.8595	0.3699	0.9946	A470	C307	1.5763323	1.3461567	0.8384533	0.4718570
638	2.5982	1.3225	-0.4025	A713	C330	2.2163811	0.9452850	-0.6878786	0.3481375
639	0.4991	2.8600	-0.4292	A862	C293	0.7212818	2.5491813	-0.2728450	0.2297852
640	1.5354	0.3582	-0.9059	A477	C330	2.2163811	0.9452850	-0.6878786	0.4953625
641	-0.7011	0.7134	0.0211	A567	C127	-1.0331492	0.0055723	0.1700299	0.3962689
642	-0.2853	2.9336	-0.3199	A890	C293	0.7212818	2.5491813	-0.2728450	0.4793518
643	1.5969	2.3923	0.4817	A861	C307	1.5763323	1.3461567	0.8384533	0.4744881
644	-0.4447	-2.5210	0.8286	A78	C144	-0.2145520	-1.5164273	0.7835631	0.4265859
645	0.2723	-1.5444	-0.9020	A178	C173	0.0988042	-1.1378972	-0.4550217	0.3423256
646	1.9285	1.2034	0.9620	A702	C307	1.5763323	1.3461567	0.8384533	0.2061570
647	0.2582	-0.9978	-0.2456	A286	C173	0.0988042	-1.1378972	-0.4550217	0.1696382
648	2.1252	2.0493	0.3052	A826	C307	1.5763323	1.3461567	0.8384533	0.5950881
649	-1.7413	-0.1005	0.9667	A480	C35	-2.1242339	-0.9715258	0.7096658	0.5036646
650	-0.4058	2.2442	0.9598	A815	C197	-0.1968420	1.3899623	0.6958189	0.4423923
651	-0.1206	1.3884	0.7951	A682	C197	-0.1968420	1.3899623	0.6958189	0.0590285
652	-0.3568	1.2439	0.7083	A658	C197	-0.1968420	1.3899623	0.6958189	0.1061671
653	1.1810	1.8537	0.9802	A771	C307	1.5763323	1.3461567	0.8384533	0.3482074
654	-0.5002	-1.5126	0.9135	A207	C144	-0.2145520	-1.5164273	0.7835631	0.1398041
655	-1.4226	1.1708	-0.9875	A706	C153	-1.0030224	1.4214296	-0.8194117	0.2794318
656	-0.9131	1.1510	0.8475	A705	C197	-0.1968420	1.3899623	0.6958189	0.3689671
657	1.0217	0.4502	0.4684	A488	C249	1.0778184	-0.1223857	0.3159433	0.2603869
658	-1.6496	-2.4492	0.3033	A41	C46	-1.0353834	-2.5511392	0.0634906	0.3186551
659	-1.5074	-1.4749	-0.9940	A203	C67	-1.4757775	-1.2955060	-0.8486053	0.1188037
660	-0.6587	-0.7569	-0.0822	A351	C127	-1.0331492	0.0055723	0.1700299	0.4630505
661	2.3789	-0.3939	0.9115	A382	C340	2.6666782	-0.1317501	0.4147766	0.3488838
662	1.0938	-0.5302	-0.6202	A363	C283	1.7808158	-0.9337703	-0.8105779	0.4269880
663	-0.3053	-2.5794	-0.8020	A60	C46	-1.0353834	-2.5511392	0.0634906	0.5412783
664	-1.1621	1.4674	0.9918	A729	C197	-0.1968420	1.3899623	0.6958189	0.4462256
665	0.9583	-0.8554	-0.6986	A294	C283	1.7808158	-0.9337703	-0.8105779	0.3376213
666	1.0541	0.5678	0.5964	A524	C249	1.0778184	-0.1223857	0.3159433	0.3314536
667	0.9612	1.9183	-0.9893	A752	C293	0.7212818	2.5491813	-0.2728450	0.5290848
668	-0.3751	2.3070	-0.9414	A832	C153	-1.0030224	1.4214296	-0.8194117	0.5451604
669	0.6537	0.7686	-0.1336	A540	C240	0.6514734	1.0103327	-0.5200428	0.2101340
670	-0.8726	-1.5054	-0.9656	A188	C67	-1.4757775	-1.2955060	-0.8486053	0.3100220
671	-2.5172	-0.2889	0.8456	A439	C35	-2.1242339	-0.9715258	0.7096658	0.4038420
672	-0.9167	1.2164	-0.8789	A676	C153	-1.0030224	1.4214296	-0.8194117	0.1169468
673	-0.8183	0.8073	-0.5259	A577	C153	-1.0030224	1.4214296	-0.8194117	0.3641212
674	0.6252	2.5840	0.7525	A850	C293	0.7212818	2.5491813	-0.2728450	0.3854152
675	-0.6411	-2.6660	-0.6704	A47	C46	-1.0353834	-2.5511392	0.0634906	0.4143449
676	-1.4442	2.5206	-0.4254	A879	C161	-1.0348261	2.5280129	0.2324966	0.3582278
677	-2.7241	1.2566	0.0043	A828	C76	-2.1614253	1.1751861	0.5762133	0.4053340
678	1.8982	1.1180	0.9792	A679	C307	1.5763323	1.3461567	0.8384533	0.2302570
679	-0.3476	1.1892	-0.6487	A642	C153	-1.0030224	1.4214296	-0.8194117	0.3527879
680	1.3832	1.1466	0.9791	A630	C307	1.5763323	1.3461567	0.8384533	0.1777786
681	-1.5060	-2.2144	-0.7350	A104	C67	-1.4757775	-1.2955060	-0.8486053	0.3542406
682	-2.1970	-1.3630	-0.8107	A183	C67	-1.4757775	-1.2955060	-0.8486053	0.2755406
683	1.1011	2.0281	-0.9515	A752	C293	0.7212818	2.5491813	-0.2728450	0.5265182
684	1.5240	-2.5769	-0.1107	A6	C193	0.8084450	-2.5111158	-0.3496015	0.3400802
685	0.7573	0.6729	-0.1608	A540	C240	0.6514734	1.0103327	-0.5200428	0.2675007
686	1.4501	-1.5178	-0.9951	A166	C283	1.7808158	-0.9337703	-0.8105779	0.3664225
687	-1.1216	0.3775	-0.5772	A532	C127	-1.0331492	0.0055723	0.1700299	0.4025362
688	1.5492	0.1055	0.8944	A468	C249	1.0778184	-0.1223857	0.3159433	0.4259080
689	0.9760	-0.2515	0.1252	A409	C249	1.0778184	-0.1223857	0.3159433	0.1405587
690	2.7805	-0.9247	0.3669	A176	C340	2.6666782	-0.1317501	0.4147766	0.3182161
691	0.4993	-2.2401	0.9555	A110	C144	-0.2145520	-1.5164273	0.7835631	0.5364872
692	-0.3001	2.9835	0.0535	A897	C161	-1.0348261	2.5280129	0.2324966	0.4564032
693	-1.9597	-0.3733	1.0000	A427	C35	-2.1242339	-0.9715258	0.7096658	0.3510313
694	-1.1709	-0.1455	0.5722	A463	C127	-1.0331492	0.0055723	0.1700299	0.2303311
695	0.0636	1.0094	-0.1503	A593	C240	0.6514734	1.0103327	-0.5200428	0.3195163
696	-2.4425	-1.7417	-0.0149	A109	C35	-2.1242339	-0.9715258	0.7096658	0.6043354
697	-1.4834	2.2833	-0.6910	A879	C153	-1.0030224	1.4214296	-0.8194117	0.4902199
698	1.8933	-1.8394	-0.7686	A95	C283	1.7808158	-0.9337703	-0.8105779	0.3533639
699	-0.5196	-1.0122	-0.5065	A298	C173	0.0988042	-1.1378972	-0.4550217	0.2651932
700	-2.8339	-0.6584	-0.4160	A379	C51	-2.2655670	0.0495469	-0.7279562	0.5294120
701	1.2057	0.1009	-0.6130	A456	C249	1.0778184	-0.1223857	0.3159433	0.4267035
702	0.8516	0.8151	-0.5707	A541	C240	0.6514734	1.0103327	-0.5200428	0.1486722
703	0.6533	-1.2453	0.8047	A211	C264	1.4868170	-1.5149655	0.8303546	0.3762790
704	-1.0793	-0.4938	0.5821	A395	C127	-1.0331492	0.0055723	0.1700299	0.3191977
705	0.7861	-0.6185	0.0208	A357	C249	1.0778184	-0.1223857	0.3159433	0.3609920
706	-2.7755	0.9662	-0.3443	A778	C76	-2.1614253	1.1751861	0.5762133	0.5811914
707	-1.4821	0.3120	0.8743	A510	C127	-1.0331492	0.0055723	0.1700299	0.4865495
708	2.1590	1.9691	0.3870	A826	C307	1.5763323	1.3461567	0.8384533	0.5523547
709	-1.6780	1.6411	-0.9378	A759	C153	-1.0030224	1.4214296	-0.8194117	0.3376788
710	-1.2191	-0.3980	0.6964	A408	C127	-1.0331492	0.0055723	0.1700299	0.3719644
711	2.7604	0.6046	-0.5639	A554	C330	2.2163811	0.9452850	-0.6878786	0.3362275
712	-1.8617	-2.3291	0.1904	A41	C46	-1.0353834	-2.5511392	0.0634906	0.3917551
713	-0.8079	-0.5996	-0.1102	A369	C127	-1.0331492	0.0055723	0.1700299	0.3702171
714	-0.6987	-0.7359	0.1709	A358	C127	-1.0331492	0.0055723	0.1700299	0.3589305
715	1.2965	-1.0996	-0.9539	A206	C283	1.7808158	-0.9337703	-0.8105779	0.2644892
716	-1.2545	1.2382	0.9714	A730	C76	-2.1614253	1.1751861	0.5762133	0.4550420
717	1.1090	-0.6640	-0.7068	A334	C283	1.7808158	-0.9337703	-0.8105779	0.3484546
718	-0.4117	-1.0055	0.4070	A310	C144	-0.2145520	-1.5164273	0.7835631	0.3615461
719	0.7448	0.6819	0.1398	A549	C240	0.6514734	1.0103327	-0.5200428	0.3605340
720	1.7770	0.1665	0.9766	A423	C307	1.5763323	1.3461567	0.8384533	0.5061570
721	1.6482	-0.4822	-0.9592	A348	C283	1.7808158	-0.9337703	-0.8105779	0.2442694
722	1.0099	0.0319	0.1441	A430	C249	1.0778184	-0.1223857	0.3159433	0.1313491
723	-1.3254	-0.4557	-0.8012	A418	C67	-1.4757775	-1.2955060	-0.8486053	0.3458630
724	-2.2024	1.4958	0.7492	A819	C76	-2.1614253	1.1751861	0.5762133	0.1781918
725	2.2684	1.9133	0.2527	A826	C307	1.5763323	1.3461567	0.8384533	0.6149881
726	0.9630	0.4460	-0.3447	A501	C240	0.6514734	1.0103327	-0.5200428	0.3504007
727	-1.2437	2.5547	-0.5405	A879	C161	-1.0348261	2.5280129	0.2324966	0.3361859
728	-1.2079	1.1582	0.9452	A687	C76	-2.1614253	1.1751861	0.5762133	0.4464994
729	-0.5154	-0.8570	0.0111	A341	C173	0.0988042	-1.1378972	-0.4550217	0.4537410
730	-0.5493	-1.0761	-0.6108	A298	C173	0.0988042	-1.1378972	-0.4550217	0.2885599
731	2.0058	2.0390	0.5099	A802	C307	1.5763323	1.3461567	0.8384533	0.4836214
732	-1.0054	0.1001	-0.1434	A482	C127	-1.0331492	0.0055723	0.1700299	0.1452356
733	-0.6455	-0.8080	-0.2591	A343	C173	0.0988042	-1.1378972	-0.4550217	0.4233744
734	-1.0379	-0.2978	0.3913	A434	C127	-1.0331492	0.0055723	0.1700299	0.1764644
735	-1.2209	-1.5068	0.9982	A167	C144	-0.2145520	-1.5164273	0.7835631	0.4102041
736	0.8193	1.1242	-0.7932	A618	C240	0.6514734	1.0103327	-0.5200428	0.1849504
737	1.8490	0.9128	0.9981	A634	C307	1.5763323	1.3461567	0.8384533	0.2885570
738	-0.3372	-2.4405	-0.8860	A60	C193	0.8084450	-2.5111158	-0.3496015	0.5842198
739	-0.2006	1.0459	-0.3546	A603	C240	0.6514734	1.0103327	-0.5200428	0.3510278
740	0.1127	-1.8314	0.9863	A148	C144	-0.2145520	-1.5164273	0.7835631	0.2816539
741	1.8791	2.2742	-0.3120	A854	C293	0.7212818	2.5491813	-0.2728450	0.4906515
742	2.5492	-1.5473	-0.1886	A85	C283	1.7808158	-0.9337703	-0.8105779	0.6679639
743	-1.1907	2.6973	0.3169	A895	C161	-1.0348261	2.5280129	0.2324966	0.1365215
744	1.5662	2.5045	-0.3002	A869	C293	0.7212818	2.5491813	-0.2728450	0.3056515
745	2.4730	-0.2776	0.8725	A382	C340	2.6666782	-0.1317501	0.4147766	0.2657505
746	1.1493	-0.1922	-0.5506	A402	C249	1.0778184	-0.1223857	0.3159433	0.3359464
747	0.5183	1.8512	-0.9970	A748	C240	0.6514734	1.0103327	-0.5200428	0.4836660
748	-0.8446	-0.9020	0.6448	A316	C144	-0.2145520	-1.5164273	0.7835631	0.4610795
749	2.4197	-1.7142	-0.2610	A50	C283	1.7808158	-0.9337703	-0.8105779	0.6562973
750	-2.1413	-1.4033	0.8284	A165	C35	-2.1242339	-0.9715258	0.7096658	0.1891915
751	-2.5379	0.6876	-0.7771	A723	C51	-2.2655670	0.0495469	-0.7279562	0.3198433
752	0.7839	-2.8918	0.0879	A4	C193	0.8084450	-2.5111158	-0.3496015	0.2809102
753	0.3511	2.4340	-0.8883	A838	C293	0.7212818	2.5491813	-0.2728450	0.3669393
754	0.1350	-1.2130	-0.6263	A248	C173	0.0988042	-1.1378972	-0.4550217	0.0941923
755	0.3113	2.8561	-0.4878	A885	C293	0.7212818	2.5491813	-0.2728450	0.3106185
756	0.2665	-1.7114	0.9634	A156	C144	-0.2145520	-1.5164273	0.7835631	0.2852872
757	1.7459	0.8381	0.9980	A559	C307	1.5763323	1.3461567	0.8384533	0.2790570
758	-1.1116	-0.1985	-0.4916	A445	C127	-1.0331492	0.0055723	0.1700299	0.3147177
759	1.1286	0.6666	-0.7245	A545	C240	0.6514734	1.0103327	-0.5200428	0.3417722
760	-0.5464	2.5419	0.8000	A835	C161	-1.0348261	2.5280129	0.2324966	0.3566055
761	-1.0319	0.1283	-0.2795	A482	C127	-1.0331492	0.0055723	0.1700299	0.1911689
762	0.6609	-1.1062	-0.7027	A253	C173	0.0988042	-1.1378972	-0.4550217	0.2804904
763	-2.0774	0.3179	-0.9948	A528	C51	-2.2655670	0.0495469	-0.7279562	0.2411213
764	-2.4430	-1.0993	0.7342	A224	C35	-2.1242339	-0.9715258	0.7096658	0.1570248
765	0.7547	-0.6989	-0.2374	A356	C173	0.0988042	-1.1378972	-0.4550217	0.4375049
766	-2.9900	0.1337	-0.1185	A525	C51	-2.2655670	0.0495469	-0.7279562	0.4726808
767	1.1471	1.1879	0.9373	A660	C307	1.5763323	1.3461567	0.8384533	0.2287786
768	-2.6938	0.1317	-0.7170	A546	C51	-2.2655670	0.0495469	-0.7279562	0.1737808
769	0.6380	1.4402	0.9053	A681	C197	-0.1968420	1.3899623	0.6958189	0.3648536
770	-0.5219	-2.7379	-0.6167	A47	C46	-1.0353834	-2.5511392	0.0634906	0.4601449
771	-1.2095	-0.9892	0.8992	A295	C35	-2.1242339	-0.9715258	0.7096658	0.3739808
772	1.9367	2.2905	-0.0298	A860	B6	1.8250643	2.3704714	0.0338500	0.0850857
773	-0.2198	-2.9918	-0.0149	A14	C46	-1.0353834	-2.5511392	0.0634906	0.4448783
774	-2.8806	-0.7633	0.1991	A368	C35	-2.1242339	-0.9715258	0.7096658	0.4917192
775	1.2701	-1.4700	-0.9984	A151	C283	1.7808158	-0.9337703	-0.8105779	0.4115892
776	1.7900	-1.6445	-0.9025	A106	C283	1.7808158	-0.9337703	-0.8105779	0.2706120
777	0.2788	0.9731	0.1561	A586	C240	0.6514734	1.0103327	-0.5200428	0.3620163
778	-0.6387	0.9864	-0.5653	A623	C153	-1.0030224	1.4214296	-0.8194117	0.3511546
779	0.2667	1.2938	0.7341	A663	C197	-0.1968420	1.3899623	0.6958189	0.1993285
780	2.8609	0.1105	-0.5052	A442	C340	2.6666782	-0.1317501	0.4147766	0.4521495
781	-1.1411	-2.2151	-0.8707	A77	C67	-1.4757775	-1.2955060	-0.8486053	0.4254554
782	0.2645	-1.7999	0.9835	A148	C144	-0.2145520	-1.5164273	0.7835631	0.3208205
783	-1.4462	1.0908	-0.9821	A706	C153	-1.0030224	1.4214296	-0.8194117	0.3121651
784	-0.7567	2.0248	0.9869	A769	C197	-0.1968420	1.3899623	0.6958189	0.4952589
785	-1.1822	0.6553	0.7613	A566	C127	-1.0331492	0.0055723	0.1700299	0.4633495
786	-1.8790	-1.9855	-0.6795	A93	C67	-1.4757775	-1.2955060	-0.8486053	0.4207739
787	-0.0835	1.0285	-0.2503	A606	C240	0.6514734	1.0103327	-0.5200428	0.3409612
788	-0.3886	2.6981	0.6877	A865	C161	-1.0348261	2.5280129	0.2324966	0.4238389
789	2.0591	2.1030	-0.3322	A833	C330	2.2163811	0.9452850	-0.6878786	0.5568916
790	-1.4258	2.0107	-0.8854	A816	C153	-1.0030224	1.4214296	-0.8194117	0.3593454
791	2.6746	0.0024	-0.7382	A420	C340	2.6666782	-0.1317501	0.4147766	0.4316828
792	1.2197	-0.6145	-0.7732	A334	C283	1.7808158	-0.9337703	-0.8105779	0.3059213
793	1.1799	2.7402	-0.1813	A877	C293	0.7212818	2.5491813	-0.2728450	0.2470607
794	1.1567	2.6821	-0.3899	A877	C293	0.7212818	2.5491813	-0.2728450	0.2284640
795	-1.4169	-0.9925	0.9628	A251	C35	-2.1242339	-0.9715258	0.7096658	0.3271474
796	-2.2685	1.4878	0.7013	A819	C76	-2.1614253	1.1751861	0.5762133	0.1815918
797	1.0089	-0.1229	0.1800	A430	C249	1.0778184	-0.1223857	0.3159433	0.0684587
798	-2.3979	0.7662	0.8558	A718	C76	-2.1614253	1.1751861	0.5762133	0.3083492
799	-1.4404	1.5012	-0.9968	A759	C153	-1.0030224	1.4214296	-0.8194117	0.2315121
800	0.1252	1.0987	0.4477	A621	C197	-0.1968420	1.3899623	0.6958189	0.2871411
801	-2.9051	0.6662	-0.1963	A734	C51	-2.2655670	0.0495469	-0.7279562	0.5959474
802	-2.8443	-0.4389	-0.4787	A379	C51	-2.2655670	0.0495469	-0.7279562	0.4388120
803	-0.9229	-1.0817	-0.8160	A275	C67	-1.4757775	-1.2955060	-0.8486053	0.2664296
804	-0.8605	0.6766	-0.4246	A551	C153	-1.0030224	1.4214296	-0.8194117	0.4273879
805	-0.9142	0.5823	-0.4009	A551	C127	-1.0331492	0.0055723	0.1700299	0.4222023
806	-0.9733	-1.6410	0.9958	A170	C144	-0.2145520	-1.5164273	0.7835631	0.3651859
807	-1.5423	-0.5428	-0.9310	A384	C67	-1.4757775	-1.2955060	-0.8486053	0.3005411
808	0.5563	-2.1322	0.9791	A110	C144	-0.2145520	-1.5164273	0.7835631	0.5273872
809	-1.5315	1.4850	-0.9911	A759	C153	-1.0030224	1.4214296	-0.8194117	0.2545788
810	-0.1740	-0.9957	0.1463	A306	C173	0.0988042	-1.1378972	-0.4550217	0.3387744
811	-0.9558	-0.7741	0.6380	A362	C127	-1.0331492	0.0055723	0.1700299	0.4416638
812	-1.1562	0.1925	0.5608	A492	C127	-1.0331492	0.0055723	0.1700299	0.2335829
813	-0.8363	0.5737	-0.1675	A550	C127	-1.0331492	0.0055723	0.1700299	0.3675023
814	-2.3997	0.2924	-0.9087	A638	C51	-2.2655670	0.0495469	-0.7279562	0.1859100
815	-1.3016	0.1869	-0.7285	A496	C51	-2.2655670	0.0495469	-0.7279562	0.3672880
816	1.1794	1.3855	-0.9836	A666	C240	0.6514734	1.0103327	-0.5200428	0.4555504
817	2.9450	-0.5316	0.1218	A205	C340	2.6666782	-0.1317501	0.4147766	0.3237161
818	1.1667	-2.7515	-0.1502	A3	C193	0.8084450	-2.5111158	-0.3496015	0.2660135
819	-1.8635	-1.8478	-0.7812	A93	C67	-1.4757775	-1.2955060	-0.8486053	0.3358073
820	-2.5402	0.4521	-0.8145	A671	C51	-2.2655670	0.0495469	-0.7279562	0.2545766
821	-1.3961	-0.0252	0.7973	A475	C127	-1.0331492	0.0055723	0.1700299	0.3403311
822	1.6055	0.5331	-0.9513	A519	C330	2.2163811	0.9452850	-0.6878786	0.4288291
823	0.7855	1.3154	-0.8838	A646	C240	0.6514734	1.0103327	-0.5200428	0.2676170
824	1.6173	1.3443	0.9947	A679	C307	1.5763323	1.3461567	0.8384533	0.0663570
825	2.1857	0.1329	0.9818	A470	C340	2.6666782	-0.1317501	0.4147766	0.4375506
826	-0.4027	-2.9450	0.2332	A20	C46	-1.0353834	-2.5511392	0.0634906	0.3987512
827	0.9464	-0.8410	0.6792	A319	C249	1.0778184	-0.1223857	0.3159433	0.4044298
828	0.9591	0.8549	-0.6989	A545	C240	0.6514734	1.0103327	-0.5200428	0.2139722
829	0.4264	-2.8695	0.4338	A24	C193	0.8084450	-2.5111158	-0.3496015	0.5079436
830	0.9074	0.4300	-0.0909	A505	C249	1.0778184	-0.1223857	0.3159433	0.3765491
831	1.0656	-2.5540	-0.6412	A38	C193	0.8084450	-2.5111158	-0.3496015	0.1972125
832	0.9906	1.2340	-0.9086	A655	C240	0.6514734	1.0103327	-0.5200428	0.3171170
833	0.9983	-0.0877	0.0661	A430	C249	1.0778184	-0.1223857	0.3159433	0.1213491
834	2.0065	1.8611	0.6762	A802	C307	1.5763323	1.3461567	0.8384533	0.3691214
835	1.8496	-0.3184	0.9924	A345	C340	2.6666782	-0.1317501	0.4147766	0.5271172
836	-0.7873	-2.4682	-0.8069	A71	C46	-1.0353834	-2.5511392	0.0634906	0.4004711
837	2.2972	1.0007	-0.8627	A664	C330	2.2163811	0.9452850	-0.6878786	0.1036851
838	0.4212	1.6303	-0.9487	A699	C240	0.6514734	1.0103327	-0.5200428	0.4262993
839	1.8060	-1.3900	-0.9603	A146	C283	1.7808158	-0.9337703	-0.8105779	0.2103787
840	-0.0192	1.6302	-0.9292	A726	C153	-1.0030224	1.4214296	-0.8194117	0.4341271
841	-2.8836	0.5040	0.3743	A683	C76	-2.1614253	1.1751861	0.5762133	0.5317580
842	0.9613	1.4100	0.9560	A675	C307	1.5763323	1.3461567	0.8384533	0.2654741
843	-0.3794	-0.9701	-0.2857	A304	C173	0.0988042	-1.1378972	-0.4550217	0.2717744
844	-1.3547	-2.5256	-0.5001	A61	C46	-1.0353834	-2.5511392	0.0634906	0.3028155
845	-1.0246	-0.2662	-0.3374	A428	C127	-1.0331492	0.0055723	0.1700299	0.2625838
846	-2.4370	-1.3451	-0.6212	A131	C67	-1.4757775	-1.2955060	-0.8486053	0.4127406
847	2.4208	1.7307	-0.2186	A767	C330	2.2163811	0.9452850	-0.6878786	0.4863709
848	0.6859	-1.4071	0.9006	A211	C264	1.4868170	-1.5149655	0.8303546	0.3263426
849	1.0868	0.7894	0.7541	A579	C307	1.5763323	1.3461567	0.8384533	0.3768808
850	0.1460	1.1172	-0.4871	A615	C240	0.6514734	1.0103327	-0.5200428	0.2150945
851	1.0309	0.1301	-0.2770	A441	C249	1.0778184	-0.1223857	0.3159433	0.2974491
852	0.9375	0.5325	0.3876	A507	C249	1.0778184	-0.1223857	0.3159433	0.2889536
853	-0.2478	1.0043	-0.2601	A603	C240	0.6514734	1.0103327	-0.5200428	0.3884163
854	0.5722	-0.8538	-0.2340	A328	C173	0.0988042	-1.1378972	-0.4550217	0.3261716
855	-2.9705	0.3954	-0.0807	A669	C51	-2.2655670	0.0495469	-0.7279562	0.5660141
856	-0.6880	0.7644	0.2366	A567	C127	-1.0331492	0.0055723	0.1700299	0.3901823
857	-1.2596	-0.7977	-0.8608	A337	C67	-1.4757775	-1.2955060	-0.8486053	0.2420594
858	1.7439	1.2310	0.9909	A679	C307	1.5763323	1.3461567	0.8384533	0.1450570
859	-1.0599	-2.5859	-0.6070	A49	C46	-1.0353834	-2.5511392	0.0634906	0.2432560
860	0.0909	-1.6516	0.9383	A148	C144	-0.2145520	-1.5164273	0.7835631	0.1984539
861	2.0308	-0.0006	-0.9995	A455	C283	1.7808158	-0.9337703	-0.8105779	0.4573589
862	-0.3798	-1.1834	-0.6533	A254	C173	0.0988042	-1.1378972	-0.4550217	0.2407951
863	-0.4064	1.9079	0.9988	A774	C197	-0.1968420	1.3899623	0.6958189	0.3434923
864	-2.0250	-0.6491	0.9920	A376	C35	-2.1242339	-0.9715258	0.7096658	0.2346646
865	1.8123	-2.3046	0.3630	A11	C264	1.4868170	-1.5149655	0.8303546	0.5274907
866	-1.4801	0.6117	0.9172	A592	C76	-2.1614253	1.1751861	0.5762133	0.5285994
867	0.5761	-1.5471	0.9371	A175	C144	-0.2145520	-1.5164273	0.7835631	0.3249539
868	-1.5165	0.5741	-0.9256	A565	C153	-1.0030224	1.4214296	-0.8194117	0.4889985
869	1.5637	0.3822	-0.9207	A477	C330	2.2163811	0.9452850	-0.6878786	0.4828625
870	1.7442	-2.3123	-0.4433	A22	C193	0.8084450	-2.5111158	-0.3496015	0.4094231
871	1.4146	2.6352	-0.1346	A869	C293	0.7212818	2.5491813	-0.2728450	0.3058607
872	2.6176	0.1761	-0.7818	A465	C330	2.2163811	0.9452850	-0.6878786	0.4214417
873	-2.5544	-1.5404	-0.1838	A129	C35	-2.1242339	-0.9715258	0.7096658	0.6308354
874	0.4846	0.9947	0.4490	A587	C240	0.6514734	1.0103327	-0.5200428	0.3838496
875	-2.3887	0.7546	-0.8631	A686	C51	-2.2655670	0.0495469	-0.7279562	0.3211100
876	-0.3608	-1.0169	0.3896	A315	C144	-0.2145520	-1.5164273	0.7835631	0.3465795
877	-1.4633	-0.3968	0.8751	A396	C35	-2.1242339	-0.9715258	0.7096658	0.4670313
878	-1.0630	0.9016	0.7954	A628	C197	-0.1968420	1.3899623	0.6958189	0.4847005
879	-1.6883	1.6248	-0.9393	A759	C153	-1.0030224	1.4214296	-0.8194117	0.3361788
880	-1.9880	0.3898	0.9997	A604	C76	-2.1614253	1.1751861	0.5762133	0.4607660
881	-2.2371	-0.7257	0.9360	A366	C35	-2.1242339	-0.9715258	0.7096658	0.1950087
882	-2.3828	-1.6542	-0.4344	A96	C67	-1.4757775	-1.2955060	-0.8486053	0.5599739
883	2.8383	-0.6031	-0.4325	A204	C340	2.6666782	-0.1317501	0.4147766	0.4967494
884	-2.9896	-0.0333	-0.1429	A525	C51	-2.2655670	0.0495469	-0.7279562	0.4639787
885	-1.2532	1.3674	0.9894	A730	C197	-0.1968420	1.3899623	0.6958189	0.4575005
886	1.4762	0.8821	0.9599	A637	C307	1.5763323	1.3461567	0.8384533	0.2285453
887	0.4488	-2.2097	0.9670	A110	C144	-0.2145520	-1.5164273	0.7835631	0.5133539
888	-0.3277	1.2964	0.7488	A658	C197	-0.1968420	1.3899623	0.6958189	0.0924671
889	-0.8363	0.6378	0.3175	A544	C127	-1.0331492	0.0055723	0.1700299	0.3255156
890	-2.7794	1.1095	-0.1211	A778	C76	-2.1614253	1.1751861	0.5762133	0.4603247
891	-1.4982	-0.6681	-0.9331	A384	C67	-1.4757775	-1.2955060	-0.8486053	0.2447744
892	2.0064	0.2239	-0.9998	A455	C330	2.2163811	0.9452850	-0.6878786	0.4144291
893	1.4153	-0.9791	0.9603	A236	C264	1.4868170	-1.5149655	0.8303546	0.2457760
894	-2.0325	1.9894	0.5363	A857	C76	-2.1614253	1.1751861	0.5762133	0.3276842
895	-1.3811	2.0926	-0.8618	A816	C153	-1.0030224	1.4214296	-0.8194117	0.3638788
896	-0.6098	1.1700	0.7326	A684	C197	-0.1968420	1.3899623	0.6958189	0.2232338
897	-2.4952	-1.1168	-0.6795	A184	C67	-1.4757775	-1.2955060	-0.8486053	0.4557446
898	0.0304	-1.9895	-0.9999	A125	C173	0.0988042	-1.1378972	-0.4550217	0.4882951
899	1.3934	0.7061	0.8990	A543	C307	1.5763323	1.3461567	0.8384533	0.2945119
900	0.2342	-2.0368	0.9987	A117	C144	-0.2145520	-1.5164273	0.7835631	0.3947539
901	0.8772	0.9646	0.7179	A594	C307	1.5763323	1.3461567	0.8384533	0.4004141
902	-2.6869	1.3327	0.0373	A828	C76	-2.1614253	1.1751861	0.5762133	0.4073006
903	2.0485	0.1805	-0.9984	A455	C330	2.2163811	0.9452850	-0.6878786	0.4143958
904	-0.3375	1.2580	-0.7166	A642	C153	-1.0030224	1.4214296	-0.8194117	0.3105879
905	-0.6048	-2.1226	0.9783	A112	C144	-0.2145520	-1.5164273	0.7835631	0.3970525
906	-1.0933	1.7274	0.9990	A762	C197	-0.1968420	1.3899623	0.6958189	0.5123589
907	0.1438	1.9673	-0.9996	A781	C153	-1.0030224	1.4214296	-0.8194117	0.6242937
908	-2.4747	0.8327	-0.7916	A723	C51	-2.2655670	0.0495469	-0.7279562	0.3519766
909	1.1076	-2.5960	0.5690	A16	C193	0.8084450	-2.5111158	-0.3496015	0.4342135
910	0.5589	1.2429	0.7707	A644	C197	-0.1968420	1.3899623	0.6958189	0.3258952
911	-1.0930	-0.6141	0.6656	A395	C127	-1.0331492	0.0055723	0.1700299	0.3916977
912	1.3891	0.2267	0.8056	A490	C249	1.0778184	-0.1223857	0.3159433	0.3833413
913	-1.5499	-2.2572	-0.6747	A61	C67	-1.4757775	-1.2955060	-0.8486053	0.4032406
914	2.7089	-1.1527	-0.3299	A124	C283	1.7808158	-0.9337703	-0.8105779	0.5425639
915	1.2016	0.4437	-0.6949	A479	C240	0.6514734	1.0103327	-0.5200428	0.4305388
916	0.7562	-2.5736	0.7309	A56	C193	0.8084450	-2.5111158	-0.3496015	0.3984102
917	1.2063	2.3102	-0.7953	A823	C293	0.7212818	2.5491813	-0.2728450	0.4154848
918	1.2973	0.2384	-0.7323	A474	C249	1.0778184	-0.1223857	0.3159433	0.5428369
919	2.1666	-0.6575	-0.9645	A231	C283	1.7808158	-0.9337703	-0.8105779	0.2719922
920	0.3088	-1.3839	0.8132	A232	C144	-0.2145520	-1.5164273	0.7835631	0.2285054
921	-2.9849	0.2803	-0.0623	A669	C51	-2.2655670	0.0495469	-0.7279562	0.5385808
922	-2.2710	-0.2862	0.9573	A443	C35	-2.1242339	-0.9715258	0.7096658	0.3599087
923	-2.2230	-0.2609	-0.9712	A422	C51	-2.2655670	0.0495469	-0.7279562	0.1987526
924	-1.1654	0.0131	0.5510	A463	C127	-1.0331492	0.0055723	0.1700299	0.1735829
925	2.0881	0.5562	0.9870	A530	C307	1.5763323	1.3461567	0.8384533	0.4834237
926	1.0017	2.8271	-0.0355	A881	C293	0.7212818	2.5491813	-0.2728450	0.2652273
927	2.2241	1.6913	0.6077	A779	C307	1.5763323	1.3461567	0.8384533	0.4078881
928	1.4506	-0.7883	0.9371	A273	C264	1.4868170	-1.5149655	0.8303546	0.2898760
929	-0.2724	1.7306	-0.9687	A755	C153	-1.0030224	1.4214296	-0.8194117	0.3963604
930	0.9006	-1.2808	-0.9008	A233	C283	1.7808158	-0.9337703	-0.8105779	0.4391559
931	-0.6270	0.7808	0.0535	A567	C127	-1.0331492	0.0055723	0.1700299	0.4326356
932	0.0206	1.0314	0.2493	A609	C197	-0.1968420	1.3899623	0.6958189	0.3408411
933	-0.1750	-1.6864	0.9525	A164	C144	-0.2145520	-1.5164273	0.7835631	0.1261539
934	-0.0966	2.6236	0.7803	A852	C197	-0.1968420	1.3899623	0.6958189	0.4727870
935	-2.1915	0.5266	0.9672	A604	C76	-2.1614253	1.1751861	0.5762133	0.3565492
936	0.3985	-2.1350	0.9851	A110	C144	-0.2145520	-1.5164273	0.7835631	0.4777205
937	-0.2908	-2.2615	0.9600	A112	C144	-0.2145520	-1.5164273	0.7835631	0.3325859
938	-0.9419	1.7507	-0.9999	A741	C153	-1.0030224	1.4214296	-0.8194117	0.1902937
939	-1.0571	1.2312	-0.9261	A701	C153	-1.0030224	1.4214296	-0.8194117	0.1169985
940	0.5496	-0.8357	0.0190	A332	C173	0.0988042	-1.1378972	-0.4550217	0.4090049
941	-1.4026	-1.7698	-0.9661	A154	C67	-1.4757775	-1.2955060	-0.8486053	0.2216554
942	-1.7156	-0.9813	-0.9997	A296	C67	-1.4757775	-1.2955060	-0.8486053	0.2350411
943	-1.1728	1.9524	-0.9607	A777	C153	-1.0030224	1.4214296	-0.8194117	0.2806788
944	1.1716	1.3992	-0.9846	A655	C240	0.6514734	1.0103327	-0.5200428	0.4578504
945	1.5494	-0.4753	-0.9253	A348	C283	1.7808158	-0.9337703	-0.8105779	0.2682027
946	0.7918	1.6351	-0.9831	A693	C240	0.6514734	1.0103327	-0.5200428	0.4093837
947	-0.6693	-2.6268	0.7034	A64	C46	-1.0353834	-2.5511392	0.0634906	0.3605512
948	-0.4149	-1.0642	-0.5140	A279	C173	0.0988042	-1.1378972	-0.4550217	0.2154599
949	1.3399	2.5298	0.5057	A839	C293	0.7212818	2.5491813	-0.2728450	0.4721815
950	-1.0850	1.2580	-0.9409	A701	C153	-1.0030224	1.4214296	-0.8194117	0.1222985
951	1.4104	-0.0125	0.8077	A431	C249	1.0778184	-0.1223857	0.3159433	0.3114080
952	-0.1689	1.2276	0.6489	A658	C197	-0.1968420	1.3899623	0.6958189	0.0790744
953	-1.2890	-0.0982	0.7070	A452	C127	-1.0331492	0.0055723	0.1700299	0.2988644
954	0.8588	-1.1465	-0.8234	A233	C173	0.0988042	-1.1378972	-0.4550217	0.3789923
955	0.9992	0.2304	0.2241	A459	C249	1.0778184	-0.1223857	0.3159433	0.1744158
956	-1.0154	0.1009	0.2007	A473	C127	-1.0331492	0.0055723	0.1700299	0.0479156
957	-1.1648	1.8204	0.9869	A762	C161	-1.0348261	2.5280129	0.2324966	0.5306634
958	2.3493	1.0052	-0.8316	A664	C330	2.2163811	0.9452850	-0.6878786	0.1121851
959	-1.6549	-2.0691	0.7604	A105	C35	-2.1242339	-0.9715258	0.7096658	0.5392141
960	-0.5279	0.8633	0.1537	A581	C127	-1.0331492	0.0055723	0.1700299	0.4597689
961	1.6959	-0.4758	0.9711	A305	C264	1.4868170	-1.5149655	0.8303546	0.4629980
962	-0.7860	-1.3001	-0.8769	A218	C67	-1.4757775	-1.2955060	-0.8486053	0.2408887
963	0.4045	0.9328	-0.1822	A572	C240	0.6514734	1.0103327	-0.5200428	0.2207830
964	2.8584	-0.1906	0.5023	A412	C340	2.6666782	-0.1317501	0.4147766	0.1126983
965	-2.1611	-1.8664	-0.5178	A79	C67	-1.4757775	-1.2955060	-0.8486053	0.5290073
966	0.9421	0.3621	-0.1362	A484	C249	1.0778184	-0.1223857	0.3159433	0.3574491
967	0.4663	-2.8048	-0.5374	A30	C193	0.8084450	-2.5111158	-0.3496015	0.2745426
968	0.1256	-1.7880	0.9782	A148	C144	-0.2145520	-1.5164273	0.7835631	0.2687872
969	2.6307	0.3229	0.7596	A489	C340	2.6666782	-0.1317501	0.4147766	0.2784839
970	1.8731	0.7602	-0.9998	A568	C330	2.2163811	0.9452850	-0.6878786	0.2800958
971	-2.7520	-0.0244	0.6590	A476	C35	-2.1242339	-0.9715258	0.7096658	0.5418526
972	2.2400	-1.9569	-0.2249	A50	C283	1.7808158	-0.9337703	-0.8105779	0.6893306
973	0.0754	1.2910	-0.7074	A645	C240	0.6514734	1.0103327	-0.5200428	0.3480327
974	2.5594	1.1582	0.5875	A725	C307	1.5763323	1.3461567	0.8384533	0.4739926
975	0.8845	-0.6161	-0.3869	A361	C173	0.0988042	-1.1378972	-0.4550217	0.4585382
976	-0.7740	-0.6682	-0.2110	A369	C127	-1.0331492	0.0055723	0.1700299	0.4379838
977	-0.8790	1.0695	-0.7880	A653	C153	-1.0030224	1.4214296	-0.8194117	0.1691212
978	-1.2881	0.0288	0.7026	A475	C127	-1.0331492	0.0055723	0.1700299	0.2702495
979	-0.6097	-1.0526	-0.6213	A298	C173	0.0988042	-1.1378972	-0.4550217	0.3200266
980	-1.4135	-2.5462	0.4095	A42	C46	-1.0353834	-2.5511392	0.0634906	0.2430217
981	-1.1947	0.2059	-0.6161	A500	C127	-1.0331492	0.0055723	0.1700299	0.3826695
982	1.8473	-2.1395	0.5626	A53	C264	1.4868170	-1.5149655	0.8303546	0.4175907
983	-1.6748	-1.1306	-0.9998	A214	C67	-1.4757775	-1.2955060	-0.8486053	0.1717077
984	0.9959	-0.8871	0.7457	A319	C264	1.4868170	-1.5149655	0.8303546	0.4011457
985	-0.5795	1.8701	0.9991	A769	C197	-0.1968420	1.3899623	0.6958189	0.3886923
986	-1.6731	2.2443	0.6009	A858	C161	-1.0348261	2.5280129	0.2324966	0.4301301
987	0.0221	1.4389	-0.8278	A690	C153	-1.0030224	1.4214296	-0.8194117	0.3503271
988	0.8051	0.6000	-0.0910	A505	C240	0.6514734	1.0103327	-0.5200428	0.3310007
989	-0.1298	-1.5035	-0.8712	A191	C173	0.0988042	-1.1378972	-0.4550217	0.3367951
990	-0.6356	-2.3483	0.9015	A100	C144	-0.2145520	-1.5164273	0.7835631	0.4569525
991	2.2303	0.8724	-0.9187	A665	C330	2.2163811	0.9452850	-0.6878786	0.1058751
992	1.0429	2.0287	-0.9597	A752	C293	0.7212818	2.5491813	-0.2728450	0.5096515
993	-0.4516	2.4733	-0.8577	A832	C153	-1.0030224	1.4214296	-0.8194117	0.5471937
994	-1.2940	0.9559	-0.9203	A651	C153	-1.0030224	1.4214296	-0.8194117	0.2857985
995	-0.9320	1.2782	0.9084	A705	C197	-0.1968420	1.3899623	0.6958189	0.3531671
996	-0.4005	-1.2427	-0.7197	A254	C173	0.0988042	-1.1378972	-0.4550217	0.2895951
997	0.0619	-2.8141	-0.5798	A25	C193	0.8084450	-2.5111158	-0.3496015	0.4265759
998	-2.3791	-1.7302	-0.3363	A96	C67	-1.4757775	-1.2955060	-0.8486053	0.6167739
999	2.2268	-1.5323	0.7111	A98	C264	1.4868170	-1.5149655	0.8303546	0.2921907
1000	-1.8225	-0.7762	-0.9998	A311	C67	-1.4757775	-1.2955060	-0.8486053	0.3390744


hist(act_pred$diff, breaks = 30, col = "blue", main = "Mean Absolute Difference", xlab = "Difference")

Figure 22: Mean Absolute Difference

HVT Scoring Cells with Layers using scoreLayeredHVT

Zubin Dowlaty, Srinivasan Sudarsanam, Somya Shambhawi

2024-01-31

1 Abstract

2 Example : HVT with the Torus dataset

3 Map A : Base Compressed Map

4 Map B : Compressed Novelty Map

4.1 Voronoi Tessellation with highlighted novelty cell

5 Map C : Compressed Map without Novelty

5.0.1 Iteration 1:

5.0.2 Iteration 2:

6 Scoring on Test Data

7 Executive Summary

8 References